Polar code encoding method and apparatus in wireless communications

Information

  • Patent Grant
  • 11811528
  • Patent Number
    11,811,528
  • Date Filed
    Friday, October 1, 2021
    3 years ago
  • Date Issued
    Tuesday, November 7, 2023
    a year ago
Abstract
This application relates to the field of wireless communications technologies, and discloses an encoding method and apparatus, to improve accuracy of reliability calculation and ordering for polarized channels. The method includes: obtaining a first sequence used to encode K to-be-encoded bits, where the first sequence includes sequence numbers of N polarized channels, the first sequence is same as a second sequence or a subset of the second sequence, the second sequence comprises sequence numbers of Nmax polarized channels, and the second sequence is the sequence shown in Sequence Q11 or Table Q11, K is a positive integer, N is a positive integer power of 2, n is equal to or greater than 5, K≤N, Nmax=1024; selecting sequence numbers of K polarized channels from the first sequence; and performing polar code encoding on K the to-be-encoded bits based on the selected sequence numbers of the K polarized channels.
Description
TECHNICAL FIELD

Embodiments of this application relate to the field of communications technologies, and in particular, to a polar code encoding method and apparatus.


BACKGROUND

As the most fundamental wireless access technology, channel coding plays a key role in ensuring reliable transmission of data. In an existing wireless communications system, channel coding is usually performed by using a turbo code, a low-density parity-check (LDPC) code, and a polar code. The turbo code cannot support information transmission at an excessively low or excessively high bit rate. For medium/short packet transmission, due to encoding/decoding characteristics of the turbo code and the LDPC code, it is very difficult for the turbo code and the LDPC code to achieve ideal performance in a case of a limited code length. In terms of implementation, the turbo code and the LDPC code have relatively high computational complexity in an encoding/decoding implementation process. The polar code is a good code that has been theoretically proved to be able to achieve the Shannon capacity and has relatively low encoding/decoding complexity, and therefore is more widely applied.


However, with rapid evolution of wireless communications systems, future communications systems such as 5th generation (5G) communications systems will have some new characteristics. For example, three most typical communication scenarios include enhanced mobile broadband (eMBB), massive machine type communications (mMTC), and ultra-reliable and low-latency communications (URLLC). The communications scenarios have higher requirements on encoding/decoding performance of the polar code.


Reliability ordering for polarized channels plays a key role in the encoding/decoding performance of the polar code. However, at present, accuracy of reliability ordering for polarized channels is not desirable, hindering further improvement of the encoding/decoding performance of the polar code during application.


SUMMARY

Embodiments of this application provide a polar code encoding method and apparatus, to improve accuracy of reliability ordering for polarized channels.


Specific technical solutions provided in the embodiments of this application are as follows:


According to a first aspect, a polar code encoding method is provided. The method includes: obtaining, by an encoding apparatus, to-be-encoded bits, where a length of the to-be-encoded bits is K, and K is a positive integer; obtaining a sequence used to encode the K to-be-encoded bits, where the sequence is denoted as a first sequence, the first sequence is used to represent an order of reliability of N polarized channels, the first sequence includes sequence numbers of the N polarized channels, the sequence numbers of the N polarized channels are arranged in the first sequence based on the reliability of the N polarized channels, N is a mother code length of a polar code, N is a positive integer power of 2, and K≤N; selecting, in descending order of the reliability, the first K sequence numbers whose reliability rank relatively high in the first sequence; and mapping to-be-encoded information bits to polarized channels corresponding to the first K sequence numbers, and performing polar code encoding on the to-be-encoded bits. Therefore, positions of the information bits and fixed bits are determined by calculating reliability of polarized channels of a polar code without considering a channel parameter and a bit rate. In this way, computational complexity of polar code encoding may be reduced.


In a possible design, the first sequence is all of or a subset of a second sequence, where the second sequence includes sequence numbers of Nmax polarized channels, the sequence numbers of the Nmax polarized channels are arranged in the second sequence based on reliability of the Nmax polarized channels, Nmax is a positive integer, Nmax≥N, and an order in which the sequence numbers of the polarized channels in the first sequence are arranged is consistent with an order in which sequence numbers less than N in the sequence numbers of the polarized channels in the second sequence are arranged.


In a possible design, the second sequence may be part or all of any sequence shown in Sequence Q1 to Sequence Q30 in the specification, the sequence numbers of the N polarized channels in the second sequence are arranged in ascending order of the reliability of the N polarized channels, and a minimum value of the sequence number of the polarized channel is 0.


In a possible design, the second sequence is part or all of any sequence shown in Table Q1 to Table Q30 in the specification the sequence numbers of the N polarized channels in the second sequence are arranged in ascending order of the reliability of the N polarized channels, and a minimum value of the sequence number of the polarized channel is 0.


In a possible design, the second sequence may be part or all of any sequence shown in Sequence Z1 to Sequence Z30 in the specification, each of the sequence numbers of the N polarized channels in the second sequence corresponds to the order of the reliability of the sequence number in the entire sequence, and a minimum value of the sequence number of the polarized channel is 0.


In a possible design, the second sequence is part or all of any sequence shown in Table Z1 to Table Z30 in the specification, each of the sequence numbers of the N polarized channels in the second sequence corresponds to the order of the reliability of the sequence number in the entire sequence, and a minimum value of the sequence number of the polarized channel is 0.


According to a second aspect, a polar code encoding apparatus is provided. The apparatus has a function of implementing the method according to any one of the first aspect and the possible designs of the first aspect. The function may be implemented by using hardware, or may be implemented by using hardware to execute corresponding software. The hardware or the software includes one or more modules corresponding to the foregoing function.


In a possible design, when part or all of the function is implemented by using hardware, the polar code encoding apparatus includes: an input interface circuit, configured to obtain to-be-encoded bits; a logic circuit, configured to perform the method according to any one of the first aspect and the possible designs of the first aspect; and an output interface circuit, configured to output a bit sequence after encoding.


Optionally, the polar code encoding apparatus may be a chip or an integrated circuit.


In a possible design, when part or all of the function is implemented by using software, the polar code encoding apparatus includes: a memory, configured to store a program; and a processor, configured to execute the program stored in the memory. When the program is executed, the polar code encoding apparatus may implement the method according to any one of the first aspect and the possible designs of the first aspect.


Optionally, the memory may be a physically independent unit. Alternatively, the memory is integrated with a processor.


In a possible design, when part or all of the function is implemented by using software, the polar code encoding apparatus includes a processor. The memory configured to store the program is located outside the encoding apparatus. The processor is connected to the memory by using a circuit/wire and is configured to read and execute the program stored in the memory.


According to a third aspect, a communications system is provided. The communications system includes a network device and a terminal. The network device or the terminal may perform the method according to any one of the first aspect and the possible designs of the first aspect.


According to a fourth aspect, a computer storage medium storing a computer program is provided. The computer program includes an instruction used to perform the method according to any one of the first aspect and the possible designs of the first aspect.


According to a fifth aspect, a computer program product including an instruction is provided. When run on a computer, the instruction causes the computer to perform the methods according to the foregoing aspects.


According to a sixth aspect, a wireless device is provided. The wireless device includes an encoding apparatus configured to implement the method described in any one of the first aspect and the possible designs of the first aspect, a modulator, and a transceiver, where

    • the modulator is configured to modulate a bit sequence after encoding, to obtain a modulated sequence; and
    • the transceiver is configured to send the modulated sequence.


In a possible design, the wireless device is a terminal or a network device.





BRIEF DESCRIPTION OF DRAWINGS


FIG. 1 is a schematic architectural diagram of a communications system applied in an embodiment of this application;



FIG. 2 is a schematic flowchart of a polar code encoding method according to an embodiment of this application;



FIG. 3 is a first schematic structural diagram of a polar code encoding apparatus according to an embodiment of this application;



FIG. 4 is a second schematic structural diagram of a polar code encoding apparatus according to an embodiment of this application;



FIG. 5 is a third schematic structural diagram of a polar code encoding apparatus according to an embodiment of this application; and



FIG. 6 is a fourth schematic structural diagram of a polar code encoding apparatus according to an embodiment of this application.





DESCRIPTION OF EMBODIMENTS

The following describes in detail the embodiments of this application with reference to accompanying drawings.


The embodiments of this application provide a polar code encoding method and apparatus. A reliability order is obtained based on reliability of polarized channels, sequence numbers of polarized channels used to send information bits are selected based on the reliability order, and polar code encoding is performed based on the sequence numbers selected for the information bits. In the embodiments of this application, a reliability of each subchannel of a polar code can be calculated more accurately. The encoding method and apparatus provided in the embodiments of the present invention are described below in detail with reference to the accompanying drawings.


To facilitate understanding of the embodiments of this application, the following describes the polar code briefly.


In an encoding scheme of the polar code, a noiseless channel is used to transmit information useful for a user, and a pure noisy channel is used to transmit agreed information or is not used to transmit information. The polar code is a linear block code, with its encoding matrix being GN and its encoding process being x1N=u1NGN, where u1N=(u1, u2, . . . , uN) is a binary row vector having a length of N (that is, code length), GN is an N×N matrix, and GN=F2⊗(log2(N)). F2⊗(log2(N)) is defined as a Kronecker (Kronecker) product of log2N matrices F2. The foregoing matrix







F
2

=


[



1


0




1


1



]

.





In the encoding process of the polar code, some bits in u1N are used to carry information and are referred to as an information bit set, and an index set of the bits is denoted as custom character. Other bits are set to fixed values pre-agreed on by a receive end and a transmit end and are referred to as a fixed bit set or a frozen bit set (frozen bits), and an index set of the other bits is represented by a complementary set custom characterc of custom character. The encoding process of the polar code is equivalent to x1N=uAGN(A)⊕uAcGN(AC), where GN(A) is a sub-matrix obtained from rows that correspond to the indexes in the set custom character in GN, and GN(AC) is a sub-matrix obtained from rows that correspond to the indexes in the set custom characterc in GN. custom character is the information bit set in u1N, and includes K information bits. Usually, various check bits including but not limited to a cyclic redundancy check (Cyclic Redundancy Check, CRC for short) bit and a parity check (Parity Check, PC for short) bit are also included in the information bit set. uAc is the fixed bit set in u1N, and includes N−K fixed bits, which are known bits. The fixed bits are usually set to 0. However, the fixed bits may be set arbitrarily provided that the receive end and the transmit end pre-agree. Therefore, an encoding output of the polar code may be simplified to: x1N=custom characterGN(custom character). Herein, ucustom character is an information bit set in u1N, and custom character is a row vector of a length K, that is, |custom character|=K, where |⋅| represents a quantity of elements in a set, and K is a size of an information block; GN(custom character) is a sub-matrix obtained by using rows that correspond to the indexes in the set custom character in the matrix GN, and GN(custom character) is a K×N matrix.


A process of constructing the polar code, that is, a process of selecting the set custom character, determines performance of the polar code. Usually, the process of constructing the polar code is: determining, based on a mother code length N, that there are a total of N polarized channels that respectively correspond to N rows of the encoding matrix, calculating reliability of the polarized channels, and using indexes of the first K polarized channels having relatively high reliability as elements of the set custom character, and indexes that correspond to the remaining N−K polarized channels are used as elements of the index set custom characterc of the fixed bits. The set custom characterdetermines positions of the information bits, and the set custom characterc determines positions of the fixed bits. A sequence number of a polarized channel is an index of the position of an information bit or a fixed bit, that is, an index of a position in u1N.


The solutions provided in the embodiments of this application relate to how to determine reliability of a polarized channel. A basic invention idea of the embodiments of this application is that reliability of the polarized channel may be represented by using a reliability. From a perspective of spectral analysis of signals, an approximation of an existing reliability to the polarized channel reliability may be understood as domain transform of a signal. Similar to Fourier transform in which transformation between a time domain and a frequency domain of a signal is implemented by using a kernel ejw, in this method, a signal is transformed from a channel sequence number domain to a reliability weight domain by using a β kernel. In the signal time-frequency analysis field, Fourier transform and wavelet transform are most commonly used. For the Fourier transform, limited by a form of the trigonometric function kernel ejw, high time domain resolution and high frequency domain resolution cannot be achieved at the same time in a signal time-frequency analysis process. For the wavelet transform, because a wavelet kernel is used and there are various forms of functions, an instantaneous change of a signal in time domain can be captured when domain transform is performed, so that both high time domain resolution and high frequency domain resolution can be achieved. In the embodiments of this application, the polarized channel reliability is estimated by using a changeable transform kernel, so that accuracy of sequence reliability estimation is improved.



FIG. 1 is a schematic structural diagram of a wireless communications network according to an embodiment of the present invention. FIG. 1 is merely an example. Other wireless networks to which the encoding method or apparatus of the embodiments of the present invention can be applied shall all fall within the protection scope of the present invention.


As shown in FIG. 1, a wireless communications network 100 includes a network device 110 and a terminal 112. When the wireless communications network 100 includes a core network 102, the network device 110 may further be connected to the core network 102. The network device 110 may further communicate with an IP network 104, for example, an Internet, a private IP network, or another data network. The network device provides a service for a terminal within coverage of the network device. For example, as shown in FIG. 1, the network device 110 provides wireless access for one or more terminals 112 within coverage of the network device 110. In addition, there may be an overlapping area between coverage of network devices, for example, the network device 110 and a network device 120. The network devices may further communicate with each other, for example, the network device 110 may communicate with the network device 120.


The foregoing network device may be a device configured to communicate with a terminal device. For example, the network device may be a base transceiver station (BTS) in a GSM system or a CDMA system, or may be a NodeB (NB) in a WCDMA system, or may further be an evolved NodeB (eNB or eNodeB) in an LTE system or a network side device in a future 5G network. Alternatively, the network device may be a relay station, an access point, an in-vehicle device, or the like. In a device to device (D2D) communications system, the network device may alternatively be a terminal that plays a role of a base station.


The foregoing terminal may refer to user equipment (UE), an access terminal, a user unit, a mobile station, a remote station, a remote terminal, a mobile device, a user terminal, a wireless communications device, a user agent, or a user apparatus. The access terminal may be a cellular phone, a cordless phone, a Session Initiation Protocol (SIP) phone, a wireless local loop (WLL) station, a personal digital assistant (PDA), a handheld device having a wireless communication function, a computing device, another processing device connected to a wireless modem, an in-vehicle device, a wearable device, a terminal device in a future 5G network, or the like. Based on a communications system architecture shown in FIG. 1, in this embodiment of this application, the polar code encoding method may be executed by the foregoing network device or terminal. The polar code encoding method may be used when the network device or the terminal serves as a transmit end to send data or information. Correspondingly, when the network device or the terminal serves as a receive end to receive data or information, a subchannel sequence needs to be determined first based on the method of the present invention. The following describes in detail the polar code encoding method provided in the embodiments of this application.


Based on the communications system architecture shown in FIG. 1, as shown in FIG. 2, a specific procedure of a polar code encoding method provided in an embodiment of this application is as follows.


Step 201. Obtain a first sequence used to encode K to-be-encoded bits.


The first sequence includes sequence numbers of N polarized channels, the sequence numbers of the N polarized channels are arranged in the first sequence based on reliability of the N polarized channels, K is a positive integer, N is a mother code length of a polar code, and N is a positive integer power of 2.


Step 202. Sequence numbers of K polarized channels are selected from the first sequence in descending order of reliability.


Step 203. Place the to-be-encoded bits based on the selected sequence numbers of the K polarized channels, and perform polar code encoding on the to-be-encoded bits.


The K to-be-encoded bits are mapped to the K polarized channels in the N polarized channels. The reliability of the K polarized channels is higher than reliability of the remaining N−K polarized channels.


Optionally, the first sequence is all of or a subset of a second sequence, the second sequence includes sequence numbers of Nmax polarized channels, the sequence numbers of the Nmax polarized channels are arranged in the second sequence based on reliability of the Nmax polarized channels, that is, an order in which the sequence numbers of the polarized channels in the first sequence are arranged is consistent with an order in which sequence numbers less than N in the sequence numbers of the polarized channels in the second sequence are arranged. Nmax may be a positive integer power of 2 or may not be a positive integer power of 2, and Nmax≥N. A manner for calculating the reliability of the Nmax polarized channels is similar to that for calculating the reliability of the N polarized channels. The arrangement based on the reliability herein may be arrangement performed in ascending order of the reliability, or may be arrangement performed in descending order of the reliability. Alternatively, the sequence numbers of the polarized channels are grouped into two or more groups, and the sequence numbers in each group are arranged in descending order or ascending order of the reliability. A specific grouping manner may be grouping based on values of sequence numbers of polarized channels or grouping based on congruent sequence numbers (for example, three groups are divided, and sequence numbers that are congruent modulo 3 are grouped into one group). This is not specifically limited herein.


Optionally, rate matching is performed, based on a target code length, on a sequence obtained after the polar code encoding.


According to the encoding method provided in this embodiment, after input information bits are received, a quantity K of to-be-encoded bits is determined based on a target code length N of a polar code. Regardless of online calculation or a manner in which calculation and storage are performed in advance, if a second sequence is known, a first sequence may be obtained from the second sequence, and when Nmax=N, the second sequence is the first sequence. The second sequence includes an order of reliability of Nmax polarized channels, where Nmax is a maximum code length supported by a communications system. Optionally, the first sequence may be obtained from a pre-stored second sequence, then information bits are determined based on the first sequence, and finally polar encoding is performed on the K to-be-encoded bits, to obtain a bit sequence obtained after the polar encoding. Therefore, positions of the information bits and fixed bits are determined by obtaining a reliability of a polarized channel of a polar code through a combination of online calculation and offline storage.


The following specifically describes a sequence of sequence numbers of polarized channels that is obtained through arrangement based on a reliability of an ith polarized channel in N (or Nmax) polarized channels. The sequence numbers of the N polarized channels may be 0 to N−1, or may be 1 to N. In this embodiment of this application, when the reliability of the ith polarized channel of the N polarized channels is determined, a value of i may be 1, 2, . . . , and N, or may be 0, 1, . . . , and N−1.


It may be understood that formulas used in the embodiments of this application are merely examples. Any solution that may be obtained by persons skilled in the art by making simple variations to the formulas without affecting performance of the formulas shall fall within the protection scope of the embodiments of this application.


For specific sequence examples, refer to the following six groups of sequences found based on different criteria. The second sequence may be part or all of any sequence shown in Sequence Q1 to Sequence Q30. These sequences may also be represented by using corresponding tables Table Q1 to Table Q30. “Reliability or sequence number of reliability” is a natural sequence of reliability in ascending order, and “polarized channel sequence number” is polarized channel sequence numbers in corresponding sequences. Herein, “part of” has three different meanings:

    • (1) Nmax is not a positive integer power of 2, but code lengths in the given examples are all positive integer powers of 2; therefore the second sequence can only be part of any sequence shown in Sequence Q1 to Sequence Q30; or
    • (2) Nmax_encoding_device supported by an encoding device is less than Nmax_protocol regulated by a protocol, and therefore only Nmax_encoding_device in any sequence shown in Sequence Q1 to Sequence Q30 needs to be selected; or
    • (3) Part of an actually used sequence having a length of Nmax is completely consistent with part of any sequence shown in Sequence Q1 to Sequence Q30.


These sequences may also be represented by using Z sequences, that is, an order of reliability of polarized channels that corresponds to a natural order of polarized channel sequence number is used as a Z sequence. To be specific, the second sequence may be part or all of any sequence shown in Sequence Z1 to Sequence Z30. Likewise, the Z sequences may also be represented by using corresponding tables Table Z1 to Table Z30, where the polarized channel sequence numbers are sequentially arranged in ascending order, and “reliability or sequence number of reliability” is a sequence number of ordering of a reliability of a polarized channel that corresponds to the polarized channel sequence number.


For example, an xth Q sequence is Sequence Qx and Table Qx, and Sequence Qx is equivalent to Table Qx. Corresponding Z sequences are Sequence Zx and Table Zx, and Sequence Zx is equivalent to Table Zx, where x=1, 2, . . . , and 30.


First group of sequences (obtained by using a criterion that comprehensively considers performance of code length of 64, 128, 256, 512, and 1024, and preferentially considers performance of a mother code length of 256).


Sequence Q1, having a sequence length of 1024:

    • [0, 1, 4, 8, 2, 16, 32, 6, 64, 512, 3, 12, 5, 18, 128, 9, 33, 17, 10, 256, 20, 34, 24, 65, 7, 36, 66, 129, 11, 40, 19, 132, 513, 13, 68, 48, 14, 72, 257, 21, 130, 26, 35, 80, 258, 136, 38, 22, 260, 516, 37, 25, 96, 67, 264, 41, 144, 28, 69, 49, 74, 160, 42, 520, 272, 192, 70, 44, 131, 81, 15, 288, 50, 134, 73, 514, 23, 52, 320, 133, 76, 82, 137, 56, 27, 259, 528, 97, 39, 384, 138, 84, 29, 261, 145, 544, 43, 98, 140, 30, 88, 262, 146, 71, 518, 265, 161, 45, 100, 148, 51, 46, 576, 75, 266, 104, 273, 164, 193, 53, 515, 162, 268, 77, 152, 274, 54, 524, 83, 57, 112, 85, 135, 289, 517, 194, 78, 290, 58, 276, 168, 530, 99, 139, 196, 86, 176, 640, 60, 89, 280, 101, 147, 292, 521, 141, 321, 142, 90, 200, 545, 31, 102, 263, 105, 529, 322, 149, 296, 47, 522, 92, 208, 267, 385, 324, 304, 536, 768, 532, 163, 153, 150, 106, 55, 165, 386, 577, 328, 548, 269, 113, 154, 79, 224, 166, 275, 108, 578, 270, 59, 114, 195, 169, 156, 87, 546, 61, 277, 291, 519, 278, 116, 170, 197, 641, 177, 281, 91, 552, 201, 388, 293, 198, 523, 62, 143, 336, 584, 172, 282, 120, 644, 103, 178, 294, 531, 202, 93, 323, 560, 392, 297, 151, 580, 209, 284, 180, 525, 107, 94, 204, 769, 298, 352, 325, 526, 155, 109, 533, 400, 305, 300, 642, 210, 184, 326, 538, 115, 167, 592, 157, 225, 306, 547, 329, 110, 770, 212, 117, 171, 550, 330, 226, 648, 387, 308, 158, 608, 416, 337, 534, 216, 271, 549, 118, 279, 537, 332, 389, 173, 579, 121, 199, 776, 179, 228, 553, 338, 656, 312, 540, 390, 174, 581, 393, 283, 772, 122, 672, 554, 784, 63, 340, 704, 448, 561, 353, 800, 394, 232, 203, 527, 582, 556, 295, 285, 181, 124, 205, 240, 643, 585, 562, 286, 299, 354, 182, 401, 211, 396, 344, 586, 832, 564, 95, 185, 206, 327, 645, 535, 402, 593, 186, 356, 588, 568, 307, 646, 418, 213, 301, 227, 302, 896, 594, 360, 111, 649, 771, 417, 539, 214, 404, 309, 188, 449, 331, 217, 159, 609, 596, 551, 650, 119, 229, 333, 408, 541, 773, 610, 657, 310, 420, 600, 218, 368, 230, 652, 391, 175, 313, 339, 542, 334, 123, 555, 774, 233, 314, 658, 612, 341, 777, 450, 220, 424, 355, 673, 583, 125, 234, 183, 395, 241, 557, 660, 616, 316, 342, 345, 778, 563, 403, 287, 397, 452, 674, 558, 785, 432, 187, 357, 207, 664, 587, 780, 705, 676, 236, 346, 565, 361, 126, 242, 589, 405, 215, 398, 566, 303, 597, 358, 801, 419, 624, 456, 786, 348, 244, 569, 189, 590, 219, 647, 311, 706, 362, 595, 464, 802, 406, 680, 421, 788, 248, 598, 190, 570, 369, 651, 409, 834, 410, 708, 480, 613, 231, 572, 315, 659, 364, 422, 335, 688, 370, 792, 221, 611, 451, 601, 425, 804, 412, 653, 453, 833, 317, 712, 235, 602, 343, 543, 372, 654, 222, 614, 426, 775, 433, 559, 237, 898, 617, 347, 808, 243, 720, 454, 665, 318, 604, 376, 661, 428, 779, 238, 675, 359, 836, 458, 625, 399, 662, 677, 434, 567, 457, 816, 245, 618, 349, 787, 127, 781, 897, 407, 666, 436, 591, 363, 620, 465, 736, 350, 678, 571, 246, 681, 249, 626, 460, 707, 840, 411, 782, 365, 789, 440, 599, 374, 668, 628, 423, 900, 466, 848, 803, 250, 790, 371, 709, 191, 573, 689, 481, 682, 413, 603, 793, 366, 713, 468, 710, 373, 574, 655, 427, 806, 414, 684, 904, 252, 615, 482, 632, 805, 429, 794, 864, 223, 690, 455, 714, 835, 472, 809, 377, 605, 619, 435, 663, 721, 319, 796, 484, 692, 912, 430, 606, 716, 488, 810, 459, 838, 667, 239, 817, 621, 378, 837, 722, 437, 696, 461, 737, 679, 380, 812, 627, 247, 899, 841, 441, 622, 928, 351, 724, 783, 469, 629, 818, 438, 669, 462, 738, 683, 251, 842, 849, 496, 901, 820, 728, 467, 633, 902, 367, 670, 791, 442, 844, 630, 474, 685, 850, 483, 691, 711, 379, 865, 795, 415, 824, 960, 740, 253, 905, 634, 444, 693, 744, 485, 807, 686, 906, 470, 575, 715, 375, 866, 913, 473, 852, 636, 797, 431, 694, 811, 486, 752, 723, 798, 489, 856, 908, 254, 717, 607, 930, 476, 697, 725, 914, 439, 819, 839, 868, 492, 718, 698, 381, 813, 623, 814, 498, 872, 739, 929, 671, 916, 821, 463, 726, 961, 843, 490, 631, 729, 700, 382, 741, 845, 920, 471, 822, 851, 730, 497, 880, 742, 443, 903, 687, 825, 500, 445, 932, 846, 635, 745, 826, 732, 446, 962, 936, 475, 853, 867, 637, 907, 487, 695, 746, 828, 753, 854, 857, 915, 964, 477, 909, 719, 799, 699, 493, 504, 748, 944, 858, 873, 638, 754, 255, 968, 869, 491, 478, 383, 910, 815, 917, 727, 870, 701, 931, 860, 499, 756, 731, 823, 922, 874, 976, 918, 502, 933, 743, 760, 881, 494, 702, 921, 876, 501, 847, 992, 447, 733, 827, 882, 934, 963, 505, 937, 747, 855, 924, 734, 829, 965, 938, 884, 506, 749, 945, 859, 755, 479, 966, 830, 888, 940, 750, 871, 970, 911, 757, 946, 969, 861, 977, 875, 919, 639, 758, 948, 862, 761, 508, 972, 923, 877, 952, 886, 935, 978, 762, 503, 883, 703, 993, 925, 878, 980, 941, 764, 495, 926, 885, 994, 735, 939, 984, 967, 889, 947, 831, 507, 942, 751, 973, 996, 890, 949, 759, 892, 971, 1000, 953, 509, 863, 981, 950, 974, 763, 1008, 979, 879, 954, 986, 995, 891, 927, 510, 765, 956, 997, 982, 887, 985, 943, 998, 1001, 766, 988, 951, 1004, 893, 1010, 957, 975, 511, 1002, 894, 983, 1009, 955, 987, 1012, 958, 999, 1005, 989, 1016, 990, 1011, 767, 1003, 1014, 1006, 1017, 895, 1013, 991, 1018, 959, 1020, 1015, 1007, 1019, 1021, 1022, 1023]












TABLE Q1, having a sequence length of 1024:










Reliability or sequence
Polarized channel



number of reliability
sequence number














1
1



2
4



3
8



4
2



5
16



6
32



7
6



8
64



9
512



10
3



11
12



12
5



13
18



14
128



15
9



16
33



17
17



18
10



19
256



20
20



21
34



22
24



23
65



24
7



25
36



26
66



27
129



28
11



29
40



30
19



31
132



32
513



33
13



34
68



35
48



36
14



37
72



38
257



39
21



40
130



41
26



42
35



43
80



44
258



45
136



46
38



47
22



48
260



49
516



50
37



51
25



52
96



53
67



54
264



55
41



56
144



57
28



58
69



59
49



60
74



61
160



62
42



63
520



64
272



65
192



66
70



67
44



68
131



69
81



70
15



71
288



72
50



73
134



74
73



75
514



76
23



77
52



78
320



79
133



80
76



81
82



82
137



83
56



84
27



85
259



86
528



87
97



88
39



89
384



90
138



91
84



92
29



93
261



94
145



95
544



96
43



97
98



98
140



99
30



100
88



101
262



102
146



103
71



104
518



105
265



106
161



107
45



108
100



109
148



110
51



111
46



112
576



113
75



114
266



115
104



116
273



117
164



118
193



119
53



120
515



121
162



122
268



123
77



124
152



125
274



126
54



127
524



128
83



129
57



130
112



131
85



132
135



133
289



134
517



135
194



136
78



137
290



138
58



139
276



140
168



141
530



142
99



143
139



144
196



145
86



146
176



147
640



148
60



149
89



150
280



151
101



152
147



153
292



154
521



155
141



156
321



157
142



158
90



159
200



160
545



161
31



162
102



163
263



164
105



165
529



166
322



167
149



168
296



169
47



170
522



171
92



172
208



173
267



174
385



175
324



176
304



177
536



178
768



179
532



180
163



181
153



182
150



183
106



184
55



185
165



186
386



187
577



188
328



189
548



190
269



191
113



192
154



193
79



194
224



195
166



196
275



197
108



198
578



199
270



200
59



201
114



202
195



203
169



204
156



205
87



206
546



207
61



208
277



209
291



210
519



211
278



212
116



213
170



214
197



215
641



216
177



217
281



218
91



219
552



220
201



221
388



222
293



223
198



224
523



225
62



226
143



227
336



228
584



229
172



230
282



231
120



232
644



233
103



234
178



235
294



236
531



237
202



238
93



239
323



240
560



241
392



242
297



243
151



244
580



245
209



246
284



247
180



248
525



249
107



250
94



251
204



252
769



253
298



254
352



255
325



256
526



257
155



258
109



259
533



260
400



261
305



262
300



263
642



264
210



265
184



266
326



267
538



268
115



269
167



270
592



271
157



272
225



273
306



274
547



275
329



276
110



277
770



278
212



279
117



280
171



281
550



282
330



283
226



284
648



285
387



286
308



287
158



288
608



289
416



290
337



291
534



292
216



293
271



294
549



295
118



296
279



297
537



298
332



299
389



300
173



301
579



302
121



303
199



304
776



305
179



306
228



307
553



308
338



309
656



310
312



311
540



312
390



313
174



314
581



315
393



316
283



317
772



318
122



319
672



320
554



321
784



322
63



323
340



324
704



325
448



326
561



327
353



328
800



329
394



330
232



331
203



332
527



333
582



334
556



335
295



336
285



337
181



338
124



339
205



340
240



341
643



342
585



343
562



344
286



345
299



346
354



347
182



348
401



349
211



350
396



351
344



352
586



353
832



354
564



355
95



356
185



357
206



358
327



359
645



360
535



361
402



362
593



363
186



364
356



365
588



366
568



367
307



368
646



369
418



370
213



371
301



372
227



373
302



374
896



375
594



376
360



377
111



378
649



379
771



380
417



381
539



382
214



383
404



384
309



385
188



386
449



387
331



388
217



389
159



390
609



391
596



392
551



393
650



394
119



395
229



396
333



397
408



398
541



399
773



400
610



401
657



402
310



403
420



404
600



405
218



406
368



407
230



408
652



409
391



410
175



411
313



412
339



413
542



414
334



415
123



416
555



417
774



418
233



419
314



420
658



421
612



422
341



423
777



424
450



425
220



426
424



427
355



428
673



429
583



430
125



431
234



432
183



433
395



434
241



435
557



436
660



437
616



438
316



439
342



440
345



441
778



442
563



443
403



444
287



445
397



446
452



447
674



448
558



449
785



450
432



451
187



452
357



453
207



454
664



455
587



456
780



457
705



458
676



459
236



460
346



461
565



462
361



463
126



464
242



465
589



466
405



467
215



468
398



469
566



470
303



471
597



472
358



473
801



474
419



475
624



476
456



477
786



478
348



479
244



480
569



481
189



482
590



483
219



484
647



485
311



486
706



487
362



488
595



489
464



490
802



491
406



492
680



493
421



494
788



495
248



496
598



497
190



498
570



499
369



500
651



501
409



502
834



503
410



504
708



505
480



506
613



507
231



508
572



509
315



510
659



511
364



512
422



513
335



514
688



515
370



516
792



517
221



518
611



519
451



520
601



521
425



522
804



523
412



524
653



525
453



526
833



527
317



528
712



529
235



530
602



531
343



532
543



533
372



534
654



535
222



536
614



537
426



538
775



539
433



540
559



541
237



542
898



543
617



544
347



545
808



546
243



547
720



548
454



549
665



550
318



551
604



552
376



553
661



554
428



555
779



556
238



557
675



558
359



559
836



560
458



561
625



562
399



563
662



564
677



565
434



566
567



567
457



568
816



569
245



570
618



571
349



572
787



573
127



574
781



575
897



576
407



577
666



578
436



579
591



580
363



581
620



582
465



583
736



584
350



585
678



586
571



587
246



588
681



589
249



590
626



591
460



592
707



593
840



594
411



595
782



596
365



597
789



598
440



599
599



600
374



601
668



602
628



603
423



604
900



605
466



606
848



607
803



608
250



609
790



610
371



611
709



612
191



613
573



614
689



615
481



616
682



617
413



618
603



619
793



620
366



621
713



622
468



623
710



624
373



625
574



626
655



627
427



628
806



629
414



630
684



631
904



632
252



633
615



634
482



635
632



636
805



637
429



638
794



639
864



640
223



641
690



642
455



643
714



644
835



645
472



646
809



647
377



648
605



649
619



650
435



651
663



652
721



653
319



654
796



655
484



656
692



657
912



658
430



659
606



660
716



661
488



662
810



663
459



664
838



665
667



666
239



667
817



668
621



669
378



670
837



671
722



672
437



673
696



674
461



675
737



676
679



677
380



678
812



679
627



680
247



681
899



682
841



683
441



684
622



685
928



686
351



687
724



688
783



689
469



690
629



691
818



692
438



693
669



694
462



695
738



696
683



697
251



698
842



699
849



700
496



701
901



702
820



703
728



704
467



705
633



706
902



707
367



708
670



709
791



710
442



711
844



712
630



713
474



714
685



715
850



716
483



717
691



718
711



719
379



720
865



721
795



722
415



723
824



724
960



725
740



726
253



727
905



728
634



729
444



730
693



731
744



732
485



733
807



734
686



735
906



736
470



737
575



738
715



739
375



740
866



741
913



742
473



743
852



744
636



745
797



746
431



747
694



748
811



749
486



750
752



751
723



752
798



753
489



754
856



755
908



756
254



757
717



758
607



759
930



760
476



761
697



762
725



763
914



764
439



765
819



766
839



767
868



768
492



769
718



770
698



771
381



772
813



773
623



774
814



775
498



776
872



777
739



778
929



779
671



780
916



781
821



782
463



783
726



784
961



785
843



786
490



787
631



788
729



789
700



790
382



791
741



792
845



793
920



794
471



795
822



796
851



797
730



798
497



799
880



800
742



801
443



802
903



803
687



804
825



805
500



806
445



807
932



808
846



809
635



810
745



811
826



812
732



813
446



814
962



815
936



816
475



817
853



818
867



819
637



820
907



821
487



822
695



823
746



824
828



825
753



826
854



827
857



828
915



829
964



830
477



831
909



832
719



833
799



834
699



835
493



836
504



837
748



838
944



839
858



840
873



841
638



842
754



843
255



844
968



845
869



846
491



847
478



848
383



849
910



850
815



851
917



852
727



853
870



854
701



855
931



856
860



857
499



858
756



859
731



860
823



861
922



862
874



863
976



864
918



865
502



866
933



867
743



868
760



869
881



870
494



871
702



872
921



873
876



874
501



875
847



876
992



877
447



878
733



879
827



880
882



881
934



882
963



883
505



884
937



885
747



886
855



887
924



888
734



889
829



890
965



891
938



892
884



893
506



894
749



895
945



896
859



897
755



898
479



899
966



900
830



901
888



902
940



903
750



904
871



905
970



906
911



907
757



908
946



909
969



910
861



911
977



912
875



913
919



914
639



915
758



916
948



917
862



918
761



919
508



920
972



921
923



922
877



923
952



924
886



925
935



926
978



927
762



928
503



929
883



930
703



931
993



932
925



933
878



934
980



935
941



936
764



937
495



938
926



939
885



940
994



941
735



942
939



943
984



944
967



945
889



946
947



947
831



948
507



949
942



950
751



951
973



952
996



953
890



954
949



955
759



956
892



957
971



958
1000



959
953



960
509



961
863



962
981



963
950



964
974



965
763



966
1008



967
979



968
879



969
954



970
986



971
995



972
891



973
927



974
510



975
765



976
956



977
997



978
982



979
887



980
985



981
943



982
998



983
1001



984
766



985
988



986
951



987
1004



988
893



989
1010



990
957



991
975



992
511



993
1002



994
894



995
983



996
1009



997
955



998
987



999
1012



1000
958



1001
999



1002
1005



1003
989



1004
1016



1005
990



1006
1011



1007
767



1008
1003



1009
1014



1010
1006



1011
1017



1012
895



1013
1013



1014
991



1015
1018



1016
959



1017
1020



1018
1015



1019
1007



1020
1019



1021
1021



1022
1022



1023
1023










Sequence Q2, having a sequence length of 512:

    • [0, 1, 4, 8, 2, 16, 32, 6, 64, 3, 12, 5, 18, 128, 9, 33, 17, 10, 256, 20, 34, 24, 65, 7, 36, 66, 129, 11, 40, 19, 132, 13, 68, 48, 14, 72, 257, 21, 130, 26, 35, 80, 258, 136, 38, 22, 260, 37, 25, 96, 67, 264, 41, 144, 28, 69, 49, 74, 160, 42, 272, 192, 70, 44, 131, 81, 15, 288, 50, 134, 73, 23, 52, 320, 133, 76, 82, 137, 56, 27, 259, 97, 39, 384, 138, 84, 29, 261, 145, 43, 98, 140, 30, 88, 262, 146, 71, 265, 161, 45, 100, 148, 51, 46, 75, 266, 104, 273, 164, 193, 53, 162, 268, 77, 152, 274, 54, 83, 57, 112, 85, 135, 289, 194, 78, 290, 58, 276, 168, 99, 139, 196, 86, 176, 60, 89, 280, 101, 147, 292, 141, 321, 142, 90, 200, 31, 102, 263, 105, 322, 149, 296, 47, 92, 208, 267, 385, 324, 304, 163, 153, 150, 106, 55, 165, 386, 328, 269, 113, 154, 79, 224, 166, 275, 108, 270, 59, 114, 195, 169, 156, 87, 61, 277, 291, 278, 116, 170, 197, 177, 281, 91, 201, 388, 293, 198, 62, 143, 336, 172, 282, 120, 103, 178, 294, 202, 93, 323, 392, 297, 151, 209, 284, 180, 107, 94, 204, 298, 352, 325, 155, 109, 400, 305, 300, 210, 184, 326, 115, 167, 157, 225, 306, 329, 110, 212, 117, 171, 330, 226, 387, 308, 158, 416, 337, 216, 271, 118, 279, 332, 389, 173, 121, 199, 179, 228, 338, 312, 390, 174, 393, 283, 122, 63, 340, 448, 353, 394, 232, 203, 295, 285, 181, 124, 205, 240, 286, 299, 354, 182, 401, 211, 396, 344, 95, 185, 206, 327, 402, 186, 356, 307, 418, 213, 301, 227, 302, 360, 111, 417, 214, 404, 309, 188, 449, 331, 217, 159, 119, 229, 333, 408, 310, 420, 218, 368, 230, 391, 175, 313, 339, 334, 123, 233, 314, 341, 450, 220, 424, 355, 125, 234, 183, 395, 241, 316, 342, 345, 403, 287, 397, 452, 432, 187, 357, 207, 236, 346, 361, 126, 242, 405, 215, 398, 303, 358, 419, 456, 348, 244, 189, 219, 311, 362, 464, 406, 421, 248, 190, 369, 409, 410, 480, 231, 315, 364, 422, 335, 370, 221, 451, 425, 412, 453, 317, 235, 343, 372, 222, 426, 433, 237, 347, 243, 454, 318, 376, 428, 238, 359, 458, 399, 434, 457, 245, 349, 127, 407, 436, 363, 465, 350, 246, 249, 460, 411, 365, 440, 374, 423, 466, 250, 371, 191, 481, 413, 366, 468, 373, 427, 414, 252, 482, 429, 223, 455, 472, 377, 435, 319, 484, 430, 488, 459, 239, 378, 437, 461, 380, 247, 441, 351, 469, 438, 462, 251, 496, 467, 367, 442, 474, 483, 379, 415, 253, 444, 485, 470, 375, 473, 431, 486, 489, 254, 476, 439, 492, 381, 498, 463, 490, 382, 471, 497, 443, 500, 445, 446, 475, 487, 477, 493, 504, 255, 491, 478, 383, 499, 502, 494, 501, 447, 505, 506, 479, 508, 503, 495, 507, 509, 510, 511]












TABLE Q2, having a sequence length of 512:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
4



3
8



4
2



5
16



6
32



7
6



8
64



9
3



10
12



11
5



12
18



13
128



14
9



15
33



16
17



17
10



18
256



19
20



20
34



21
24



22
65



23
7



24
36



25
66



26
129



27
11



28
40



29
19



30
132



31
13



32
68



33
48



34
14



35
72



36
257



37
21



38
130



39
26



40
35



41
80



42
258



43
136



44
38



45
22



46
260



47
37



48
25



49
96



50
67



51
264



52
41



53
144



54
28



55
69



56
49



57
74



58
160



59
42



60
272



61
192



62
70



63
44



64
131



65
81



66
15



67
288



68
50



69
134



70
73



71
23



72
52



73
320



74
133



75
76



76
82



77
137



78
56



79
27



80
259



81
97



82
39



83
384



84
138



85
84



86
29



87
261



88
145



89
43



90
98



91
140



92
30



93
88



94
262



95
146



96
71



97
265



98
161



99
45



100
100



101
148



102
51



103
46



104
75



105
266



106
104



107
273



108
164



109
193



110
53



111
162



112
268



113
77



114
152



115
274



116
54



117
83



118
57



119
112



120
85



121
135



122
289



123
194



124
78



125
290



126
58



127
276



128
168



129
99



130
139



131
196



132
86



133
176



134
60



135
89



136
280



137
101



138
147



139
292



140
141



141
321



142
142



143
90



144
200



145
31



146
102



147
263



148
105



149
322



150
149



151
296



152
47



153
92



154
208



155
267



156
385



157
324



158
304



159
163



160
153



161
150



162
106



163
55



164
165



165
386



166
328



167
269



168
113



169
154



170
79



171
224



172
166



173
275



174
108



175
270



176
59



177
114



178
195



179
169



180
156



181
87



182
61



183
277



184
291



185
278



186
116



187
170



188
197



189
177



190
281



191
91



192
201



193
388



194
293



195
198



196
62



197
143



198
336



199
172



200
282



201
120



202
103



203
178



204
294



205
202



206
93



207
323



208
392



209
297



210
151



211
209



212
284



213
180



214
107



215
94



216
204



217
298



218
352



219
325



220
155



221
109



222
400



223
305



224
300



225
210



226
184



227
326



228
115



229
167



230
157



231
225



232
306



233
329



234
110



235
212



236
117



237
171



238
330



239
226



240
387



241
308



242
158



243
416



244
337



245
216



246
271



247
118



248
279



249
332



250
389



251
173



252
121



253
199



254
179



255
228



256
338



257
312



258
390



259
174



260
393



261
283



262
122



263
63



264
340



265
448



266
353



267
394



268
232



269
203



270
295



271
285



272
181



273
124



274
205



275
240



276
286



277
299



278
354



279
182



280
401



281
211



282
396



283
344



284
95



285
185



286
206



287
327



288
402



289
186



290
356



291
307



292
418



293
213



294
301



295
227



296
302



297
360



298
111



299
417



300
214



301
404



302
309



303
188



304
449



305
331



306
217



307
159



308
119



309
229



310
333



311
408



312
310



313
420



314
218



315
368



316
230



317
391



318
175



319
313



320
339



321
334



322
123



323
233



324
314



325
341



326
450



327
220



328
424



329
355



330
125



331
234



332
183



333
395



334
241



335
316



336
342



337
345



338
403



339
287



340
397



341
452



342
432



343
187



344
357



345
207



346
236



347
346



348
361



349
126



350
242



351
405



352
215



353
398



354
303



355
358



356
419



357
456



358
348



359
244



360
189



361
219



362
311



363
362



364
464



365
406



366
421



367
248



368
190



369
369



370
409



371
410



372
480



373
231



374
315



375
364



376
422



377
335



378
370



379
221



380
451



381
425



382
412



383
453



384
317



385
235



386
343



387
372



388
222



389
426



390
433



391
237



392
347



393
243



394
454



395
318



396
376



397
428



398
238



399
359



400
458



401
399



402
434



403
457



404
245



405
349



406
127



407
407



408
436



409
363



410
465



411
350



412
246



413
249



414
460



415
411



416
365



417
440



418
374



419
423



420
466



421
250



422
371



423
191



424
481



425
413



426
366



427
468



428
373



429
427



430
414



431
252



432
482



433
429



434
223



435
455



436
472



437
377



438
435



439
319



440
484



441
430



442
488



443
459



444
239



445
378



446
437



447
461



448
380



449
247



450
441



451
351



452
469



453
438



454
462



455
251



456
496



457
467



458
367



459
442



460
474



461
483



462
379



463
415



464
253



465
444



466
485



467
470



468
375



469
473



470
431



471
486



472
489



473
254



474
476



475
439



476
492



477
381



478
498



479
463



480
490



481
382



482
471



483
497



484
443



485
500



486
445



487
446



488
475



489
487



490
477



491
493



492
504



493
255



494
491



495
478



496
383



497
499



498
502



499
494



500
501



501
447



502
505



503
506



504
479



505
508



506
503



507
495



508
507



509
509



510
510



511
511










Sequence Q3, having a sequence length of 256:

    • [0, 1, 4, 8, 2, 16, 32, 6, 64, 3, 12, 5, 18, 128, 9, 33, 17, 10, 20, 34, 24, 65, 7, 36, 66, 129, 11, 40, 19, 132, 13, 68, 48, 14, 72, 21, 130, 26, 35, 80, 136, 38, 22, 37, 25, 96, 67, 41, 144, 28, 69, 49, 74, 160, 42, 192, 70, 44, 131, 81, 15, 50, 134, 73, 23, 52, 133, 76, 82, 137, 56, 27, 97, 39, 138, 84, 29, 145, 43, 98, 140, 30, 88, 146, 71, 161, 45, 100, 148, 51, 46, 75, 104, 164, 193, 53, 162, 77, 152, 54, 83, 57, 112, 85, 135, 194, 78, 58, 168, 99, 139, 196, 86, 176, 60, 89, 101, 147, 141, 142, 90, 200, 31, 102, 105, 149, 47, 92, 208, 163, 153, 150, 106, 55, 165, 113, 154, 79, 224, 166, 108, 59, 114, 195, 169, 156, 87, 61, 116, 170, 197, 177, 91, 201, 198, 62, 143, 172, 120, 103, 178, 202, 93, 151, 209, 180, 107, 94, 204, 155, 109, 210, 184, 115, 167, 157, 225, 110, 212, 117, 171, 226, 158, 216, 118, 173, 121, 199, 179, 228, 174, 122, 63, 232, 203, 181, 124, 205, 240, 182, 211, 95, 185, 206, 186, 213, 227, 111, 214, 188, 217, 159, 119, 229, 218, 230, 175, 123, 233, 220, 125, 234, 183, 241, 187, 207, 236, 126, 242, 215, 244, 189, 219, 248, 190, 231, 221, 235, 222, 237, 243, 238, 245, 127, 246, 249, 250, 191, 252, 223, 239, 247, 251, 253, 254, 255]









TABLE Q3







having a sequence length of 256:










Polarized
Reliability



channel
or sequence



sequence
number of



number
reliability














0
0



1
1



2
4



3
8



4
2



5
16



6
32



7
6



8
64



9
3



10
12



11
5



12
18



13
128



14
9



15
33



16
17



17
10



18
20



19
34



20
24



21
65



22
7



23
36



24
66



25
129



26
11



27
40



28
19



29
132



30
13



31
68



32
48



33
14



34
72



35
21



36
130



37
26



38
35



39
80



40
136



41
38



42
22



43
37



44
25



45
96



46
67



47
41



48
144



49
28



50
69



51
49



52
74



53
160



54
42



55
192



56
70



57
44



58
131



59
81



60
15



61
50



62
134



63
73



64
23



65
52



66
133



67
76



68
82



69
137



70
56



71
27



72
97



73
39



74
138



75
84



76
29



77
145



78
43



79
98



80
140



81
30



82
88



83
146



84
71



85
161



86
45



87
100



88
148



89
51



90
46



91
75



92
104



93
164



94
193



95
53



96
162



97
77



98
152



99
54



100
83



101
57



102
112



103
85



104
135



105
194



106
78



107
58



108
168



109
99



110
139



111
196



112
86



113
176



114
60



115
89



116
101



117
147



118
141



119
142



120
90



121
200



122
31



123
102



124
105



125
149



126
47



127
92



128
208



129
163



130
153



131
150



132
106



133
55



134
165



135
113



136
154



137
79



138
224



139
166



140
108



141
59



142
114



143
195



144
169



145
156



146
87



147
61



148
116



149
170



150
197



151
177



152
91



153
201



154
198



155
62



156
143



157
172



158
120



159
103



160
178



161
202



162
93



163
151



164
209



165
180



166
107



167
94



168
204



169
155



170
109



171
210



172
184



173
115



174
167



175
157



176
225



177
110



178
212



179
117



180
171



181
226



182
158



183
216



184
118



185
173



186
121



187
199



188
179



189
228



190
174



191
122



192
63



193
232



194
203



195
181



196
124



197
205



198
240



199
182



200
211



201
95



202
185



203
206



204
186



205
213



206
227



207
111



208
214



209
188



210
217



211
159



212
119



213
229



214
218



215
230



216
175



217
123



218
233



219
220



220
125



221
234



222
183



223
241



224
187



225
207



226
236



227
126



228
242



229
215



230
244



231
189



232
219



233
248



234
190



235
231



236
221



237
235



238
222



239
237



240
243



241
238



242
245



243
127



244
246



245
249



246
250



247
191



248
252



249
223



250
239



251
247



252
251



253
253



254
254



255
255










Sequence Q4, having a sequence length of 128:

    • [0, 1, 4, 8, 2, 16, 32, 6, 64, 3, 12, 5, 18, 9, 33, 17, 10, 20, 34, 24, 65, 7, 36, 66, 11, 40, 19, 13, 68, 48, 14, 72, 21, 26, 35, 80, 38, 22, 37, 25, 96, 67, 41, 28, 69, 49, 74, 42, 70, 44, 81, 15, 50, 73, 23, 52, 76, 82, 56, 27, 97, 39, 84, 29, 43, 98, 30, 88, 71, 45, 100, 51, 46, 75, 104, 53, 77, 54, 83, 57, 112, 85, 78, 58, 99, 86, 60, 89, 101, 90, 31, 102, 105, 47, 92, 106, 55, 113, 79, 108, 59, 114, 87, 61, 116, 91, 62, 120, 103, 93, 107, 94, 109, 115, 110, 117, 118, 121, 122, 63, 124, 95, 111, 119, 123, 125, 126, 127]









TABLE Q4







having a sequence length of 128:










Reliability or
Polarized



sequence
channel



number of
sequence



reliability
number














0
0



1
1



2
4



3
8



4
2



5
16



6
32



7
6



8
64



9
3



10
12



11
5



12
18



13
9



14
33



15
17



16
10



17
20



18
34



19
24



20
65



21
7



22
36



23
66



24
11



25
40



26
19



27
13



28
68



29
48



30
14



31
72



32
21



33
26



34
35



35
80



36
38



37
22



38
37



39
25



40
96



41
67



42
41



43
28



44
69



45
49



46
74



47
42



48
70



49
44



50
81



51
15



52
50



53
73



54
23



55
52



56
76



57
82



58
56



59
27



60
97



61
39



62
84



63
29



64
43



65
98



66
30



67
88



68
71



69
45



70
100



71
51



72
46



73
75



74
104



75
53



76
77



77
54



78
83



79
57



80
112



81
85



82
78



83
58



84
99



85
86



86
60



87
89



88
101



89
90



90
31



91
102



92
105



93
47



94
92



95
106



96
55



97
113



98
79



99
108



100
59



101
114



102
87



103
61



104
116



105
91



106
62



107
120



108
103



109
93



110
107



111
94



112
109



113
115



114
110



115
117



116
118



117
121



118
122



119
63



120
124



121
95



122
111



123
119



124
123



125
125



126
126



127
127










Sequence Q5, having a sequence length of 64:

    • [0, 1, 4, 8, 2, 16, 32, 6, 3, 12, 5, 18, 9, 33, 17, 10, 20, 34, 24, 7, 36, 11, 40, 19, 13, 48, 14, 21, 26, 35, 38, 22, 37, 25, 41, 28, 49, 42, 44, 15, 50, 23, 52, 56, 27, 39, 29, 43, 30, 45, 51, 46, 53, 54, 57, 58, 60, 31, 47, 55, 59, 61, 62, 63]












TABLE Q5, having a sequence length of 64:










Reliability or sequence
Polarized channel



number of relability
sequence number














0
0



1
1



2
4



3
8



4
2



5
16



6
32



7
6



8
3



9
12



10
5



11
18



12
9



13
33



14
17



15
10



16
20



17
34



18
24



19
7



20
36



21
11



22
40



23
19



24
13



25
48



26
14



27
21



28
26



29
35



30
38



31
22



32
37



33
25



34
41



35
28



36
49



37
42



38
44



39
15



40
50



41
23



42
52



43
56



44
27



45
39



46
29



47
43



48
30



49
45



50
51



51
46



52
53



53
54



54
57



55
58



56
60



57
31



58
47



59
55



60
59



61
61



62
62



63
63










Sequence Z1, having a sequence length of 1024:

    • [0, 1, 4, 10, 2, 12, 7, 24, 3, 15, 18, 28, 11, 33, 36, 70, 5, 17, 13, 30, 20, 39, 47, 76, 22, 51, 41, 84, 57, 92, 99, 161, 6, 16, 21, 42, 25, 50, 46, 88, 29, 55, 62, 96, 67, 107, 111, 169, 35, 59, 72, 110, 77, 119, 126, 184, 83, 129, 138, 200, 148, 207, 225, 322, 8, 23, 26, 53, 34, 58, 66, 103, 37, 74, 60, 113, 80, 123, 136, 193, 43, 69, 81, 128, 91, 131, 145, 205, 100, 149, 158, 218, 171, 238, 250, 355, 52, 87, 97, 142, 108, 151, 162, 233, 115, 164, 183, 249, 197, 258, 276, 377, 130, 191, 201, 268, 212, 279, 295, 394, 231, 302, 318, 415, 338, 430, 463, 573, 14, 27, 40, 68, 31, 79, 73, 132, 45, 82, 90, 143, 98, 155, 157, 226, 56, 94, 102, 152, 109, 167, 182, 243, 124, 181, 192, 257, 204, 271, 287, 389, 61, 106, 121, 180, 117, 185, 195, 269, 140, 203, 213, 280, 229, 300, 313, 410, 146, 216, 234, 305, 247, 337, 347, 432, 265, 356, 363, 451, 385, 481, 497, 612, 65, 118, 135, 202, 144, 214, 223, 303, 159, 220, 237, 331, 251, 339, 357, 453, 172, 245, 264, 349, 278, 370, 382, 467, 292, 388, 405, 483, 425, 517, 535, 640, 194, 272, 283, 372, 306, 395, 407, 507, 330, 418, 431, 529, 459, 541, 556, 666, 340, 434, 464, 546, 479, 569, 587, 680, 495, 589, 608, 697, 632, 726, 756, 843, 19, 38, 44, 85, 48, 93, 101, 163, 54, 105, 114, 173, 122, 190, 199, 293, 64, 116, 125, 196, 139, 208, 211, 296, 150, 217, 230, 316, 246, 336, 344, 444, 71, 133, 137, 209, 153, 222, 235, 335, 168, 242, 253, 345, 262, 371, 373, 470, 176, 261, 273, 367, 286, 384, 402, 485, 310, 411, 419, 509, 438, 527, 550, 653, 78, 156, 166, 239, 175, 255, 266, 358, 188, 275, 282, 387, 298, 396, 414, 513, 227, 290, 308, 412, 323, 422, 439, 531, 351, 440, 460, 544, 478, 571, 584, 686, 254, 327, 346, 427, 364, 452, 472, 558, 376, 462, 487, 580, 511, 596, 620, 707, 406, 499, 515, 610, 533, 624, 600, 739, 552, 647, 669, 719, 677, 771, 790, 848, 89, 174, 186, 285, 221, 299, 312, 409, 241, 315, 329, 433, 350, 445, 468, 562, 260, 348, 361, 443, 383, 466, 491, 576, 397, 501, 503, 594, 523, 617, 629, 722, 289, 380, 369, 474, 403, 493, 512, 603, 426, 521, 537, 627, 554, 637, 658, 746, 450, 539, 565, 650, 578, 672, 692, 764, 598, 683, 710, 801, 729, 806, 813, 877, 325, 386, 424, 519, 446, 525, 548, 642, 476, 567, 560, 663, 591, 674, 694, 782, 489, 582, 605, 704, 622, 689, 736, 794, 645, 742, 713, 816, 760, 830, 847, 898, 505, 615, 634, 716, 655, 732, 749, 821, 661, 753, 786, 846, 768, 835, 870, 937, 700, 798, 775, 857, 805, 874, 865, 928, 836, 883, 893, 948, 919, 960, 974, 992, 9, 32, 75, 120, 49, 134, 104, 210, 63, 154, 170, 224, 127, 248, 256, 332, 86, 165, 141, 236, 179, 259, 291, 360, 177, 297, 267, 381, 311, 398, 413, 532, 95, 160, 206, 274, 189, 294, 281, 392, 219, 307, 320, 416, 334, 435, 448, 540, 240, 326, 343, 442, 354, 461, 469, 566, 366, 480, 498, 586, 508, 613, 625, 737, 112, 187, 198, 301, 244, 314, 333, 429, 228, 342, 352, 455, 365, 465, 482, 579, 270, 362, 375, 488, 391, 471, 496, 599, 404, 520, 530, 618, 551, 648, 659, 758, 288, 390, 400, 518, 421, 506, 536, 633, 437, 543, 570, 649, 581, 668, 684, 773, 475, 561, 590, 679, 602, 690, 712, 787, 635, 705, 728, 809, 744, 819, 841, 914, 147, 215, 263, 341, 232, 359, 368, 484, 284, 378, 393, 500, 408, 524, 534, 626, 309, 401, 420, 510, 436, 553, 563, 651, 454, 549, 577, 665, 601, 693, 708, 779, 319, 428, 447, 557, 458, 564, 585, 676, 492, 588, 616, 696, 630, 714, 734, 803, 514, 614, 641, 717, 656, 730, 747, 822, 673, 761, 770, 834, 789, 854, 871, 930, 324, 457, 486, 592, 504, 611, 623, 718, 528, 621, 643, 738, 660, 757, 769, 832, 547, 652, 671, 751, 687, 762, 783, 852, 703, 788, 797, 859, 812, 878, 888, 941, 583, 675, 695, 777, 725, 791, 800, 867, 731, 810, 823, 885, 837, 894, 903, 950, 750, 825, 842, 897, 858, 907, 915, 955, 868, 918, 927, 965, 936, 975, 984, 1007, 178, 252, 277, 379, 317, 399, 417, 538, 304, 423, 441, 555, 456, 574, 595, 688, 321, 449, 477, 572, 494, 597, 609, 709, 516, 619, 638, 721, 654, 745, 752, 833, 328, 473, 490, 607, 522, 636, 628, 733, 545, 646, 662, 748, 678, 772, 774, 850, 568, 667, 691, 765, 702, 781, 795, 860, 723, 804, 811, 879, 824, 889, 900, 947, 353, 526, 502, 644, 559, 670, 664, 766, 593, 682, 698, 785, 711, 792, 808, 875, 606, 699, 715, 796, 743, 817, 826, 886, 754, 827, 839, 896, 856, 910, 917, 961, 639, 720, 740, 818, 767, 845, 853, 904, 776, 840, 862, 912, 873, 922, 933, 968, 799, 869, 880, 929, 892, 939, 924, 979, 901, 945, 953, 972, 956, 988, 994, 1012, 374, 575, 542, 681, 604, 701, 706, 802, 631, 727, 735, 820, 755, 831, 849, 906, 657, 741, 763, 828, 780, 851, 864, 913, 793, 872, 861, 921, 887, 932, 938, 973, 685, 778, 759, 855, 807, 866, 881, 925, 815, 884, 891, 942, 902, 935, 949, 981, 838, 895, 908, 946, 916, 954, 963, 986, 923, 959, 969, 997, 976, 990, 1000, 1016, 724, 784, 814, 882, 829, 890, 899, 944, 844, 909, 905, 957, 920, 951, 964, 991, 863, 911, 926, 967, 934, 962, 978, 995, 943, 980, 970, 998, 985, 1003, 1005, 1014, 876, 931, 940, 971, 952, 977, 982, 1001, 958, 983, 993, 1008, 987, 1002, 1010, 1019, 966, 996, 989, 1006, 999, 1013, 1009, 1018, 1004, 1011, 1015, 1020, 1017, 1021, 1022, 1023]












TABLE Z1, having a sequence length of 1024:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
4



3
10



4
2



5
12



6
7



7
24



8
3



9
15



10
18



11
28



12
11



13
33



14
36



15
70



16
5



17
17



18
13



19
30



20
20



21
39



22
47



23
76



24
22



25
51



26
41



27
84



28
57



29
92



30
99



31
161



32
6



33
16



34
21



35
42



36
25



37
50



38
46



39
88



40
29



41
55



42
62



43
96



44
67



45
107



46
111



47
169



48
35



49
59



50
72



51
110



52
77



53
119



54
126



55
184



56
83



57
129



58
138



59
200



60
148



61
207



62
225



63
322



64
8



65
23



66
26



67
53



68
34



69
58



70
66



71
103



72
37



73
74



74
60



75
113



76
80



77
123



78
136



79
193



80
43



81
69



82
81



83
128



84
91



85
131



86
145



87
205



88
100



89
149



90
158



91
218



92
171



93
238



94
250



95
355



96
52



97
87



98
97



99
142



100
108



101
151



102
162



103
233



104
115



105
164



106
183



107
249



108
197



109
258



110
276



111
377



112
130



113
191



114
201



115
268



116
212



117
279



118
295



119
394



120
231



121
302



122
318



123
415



124
338



125
430



126
463



127
573



128
14



129
27



130
40



131
68



132
31



133
79



134
73



135
132



136
45



137
82



138
90



139
143



140
98



141
155



142
157



143
226



144
56



145
94



146
102



147
152



148
109



149
167



150
182



151
243



152
124



153
181



154
192



155
257



156
204



157
271



158
287



159
389



160
61



161
106



162
121



163
180



164
117



165
185



166
195



167
269



168
140



169
203



170
213



171
280



172
229



173
300



174
313



175
410



176
146



177
216



178
234



179
305



180
247



181
337



182
347



183
432



184
265



185
356



186
363



187
451



188
385



189
481



190
497



191
612



192
65



193
118



194
135



195
202



196
144



197
214



198
223



199
303



200
159



201
220



202
237



203
331



204
251



205
339



206
357



207
453



208
172



209
245



210
264



211
349



212
278



213
370



214
382



215
467



216
292



217
388



218
405



219
483



220
425



221
517



222
535



223
640



224
194



225
272



226
283



227
372



228
306



229
395



230
407



231
507



232
330



233
418



234
431



235
529



236
459



237
541



238
556



239
666



240
340



241
434



242
464



243
546



244
479



245
569



246
587



247
680



248
495



249
589



250
608



251
697



252
632



253
726



254
756



255
843



256
19



257
38



258
44



259
85



260
48



261
93



262
101



263
163



264
54



265
105



266
114



267
173



268
122



269
190



270
199



271
293



272
64



273
116



274
125



275
196



276
139



277
208



278
211



279
296



280
150



281
217



282
230



283
316



284
246



285
336



286
344



287
444



288
71



289
133



290
137



291
209



292
153



293
222



294
235



295
335



296
168



297
242



298
253



299
345



300
262



301
371



302
373



303
470



304
176



305
261



306
273



307
367



308
286



309
384



310
402



311
485



312
310



313
411



314
419



315
509



316
438



317
527



318
550



319
653



320
78



321
156



322
166



323
239



324
175



325
255



326
266



327
358



328
188



329
275



330
282



331
387



332
298



333
396



334
414



335
513



336
227



337
290



338
308



339
412



340
323



341
422



342
439



343
531



344
351



345
440



346
460



347
544



348
478



349
571



350
584



351
686



352
254



353
327



354
346



355
427



356
364



357
452



358
472



359
558



360
376



361
462



362
487



363
580



364
511



365
596



366
620



367
707



368
406



369
499



370
515



371
610



372
533



373
624



374
600



375
739



376
552



377
647



378
669



379
719



380
677



381
771



382
790



383
848



384
89



385
174



386
186



387
285



388
221



389
299



390
312



391
409



392
241



393
315



394
329



395
433



396
350



397
445



398
468



399
562



400
260



401
348



402
361



403
443



404
383



405
466



406
491



407
576



408
397



409
501



410
503



411
594



412
523



413
617



414
629



415
722



416
289



417
380



418
369



419
474



420
403



421
493



422
512



423
603



424
426



425
521



426
537



427
627



428
554



429
637



430
658



431
746



432
450



433
539



434
565



435
650



436
578



437
672



438
692



439
764



440
598



441
683



442
710



443
801



444
729



445
806



446
813



447
877



448
325



449
386



450
424



451
519



452
446



453
525



454
548



455
642



456
476



457
567



458
560



459
663



460
591



461
674



462
694



463
782



464
489



465
582



466
605



467
704



468
622



469
689



470
736



471
794



472
645



473
742



474
713



475
816



476
760



477
830



478
847



479
898



480
505



481
615



482
634



483
716



484
655



485
732



486
749



487
821



488
661



489
753



490
786



491
846



492
768



493
835



494
870



495
937



496
700



497
798



498
775



499
857



500
805



501
874



502
865



503
928



504
836



505
883



506
893



507
948



508
919



509
960



510
974



511
992



512
9



513
32



514
75



515
120



516
49



517
134



518
104



519
210



520
63



521
154



522
170



523
224



524
127



525
248



526
256



527
332



528
86



529
165



530
141



531
236



532
179



533
259



534
291



535
360



536
177



537
297



538
267



539
381



540
311



541
398



542
413



543
532



544
95



545
160



546
206



547
274



548
189



549
294



550
281



551
392



552
219



553
307



554
320



555
416



556
334



557
435



558
448



559
540



560
240



561
326



562
343



563
442



564
354



565
461



566
469



567
566



568
366



569
480



570
498



571
586



572
508



573
613



574
625



575
737



576
112



577
187



578
198



579
301



580
244



581
314



582
333



583
429



584
228



585
342



586
352



587
455



588
365



589
465



590
482



591
579



592
270



593
362



594
375



595
488



596
391



597
471



598
496



599
599



600
404



601
520



602
530



603
618



604
551



605
648



606
659



607
758



608
288



609
390



610
400



611
518



612
421



613
506



614
536



615
633



616
437



617
543



618
570



619
649



620
581



621
668



622
684



623
773



624
475



625
561



626
590



627
679



628
602



629
690



630
712



631
787



632
635



633
705



634
728



635
809



636
744



637
819



638
841



639
914



640
147



641
215



642
263



643
341



644
232



645
359



646
368



647
484



648
284



649
378



650
393



651
500



652
408



653
524



654
534



655
626



656
309



657
401



658
420



659
510



660
436



661
553



662
563



663
651



664
454



665
549



666
577



667
665



668
601



669
693



670
708



671
779



672
319



673
428



674
447



675
557



676
458



677
564



678
585



679
676



680
492



681
588



682
616



683
696



684
630



685
714



686
734



687
803



688
514



689
614



690
641



691
717



692
656



693
730



694
747



695
822



696
673



697
761



698
770



699
834



700
789



701
854



702
871



703
930



704
324



705
457



706
486



707
592



708
504



709
611



710
623



711
718



712
528



713
621



714
643



715
738



716
660



717
757



718
769



719
832



720
547



721
652



722
671



723
751



724
687



725
762



726
783



727
852



728
703



729
788



730
797



731
859



732
812



733
878



734
888



735
941



736
583



737
675



738
695



739
777



740
725



741
791



742
800



743
867



744
731



745
810



746
823



747
885



748
837



749
894



750
903



751
950



752
750



753
825



754
842



755
897



756
858



757
907



758
915



759
955



760
868



761
918



762
927



763
965



764
936



765
975



766
984



767
1007



768
178



769
252



770
277



771
379



772
317



773
399



774
417



775
538



776
304



777
423



778
441



779
555



780
456



781
574



782
595



783
688



784
321



785
449



786
477



787
572



788
494



789
597



790
609



791
709



792
516



793
619



794
638



795
721



796
654



797
745



798
752



799
833



800
328



801
473



802
490



803
607



804
522



805
636



806
628



807
733



808
545



809
646



810
662



811
748



812
678



813
772



814
774



815
850



816
568



817
667



818
691



819
765



820
702



821
781



822
795



823
860



824
723



825
804



826
811



827
879



828
824



829
889



830
900



831
947



832
353



833
526



834
502



835
644



836
559



837
670



838
664



839
766



840
593



841
682



842
698



843
785



844
711



845
792



846
808



847
875



848
606



849
699



850
715



851
796



852
743



853
817



854
826



855
886



856
754



857
827



858
839



859
896



860
856



861
910



862
917



863
961



864
639



865
720



866
740



867
818



868
767



869
845



870
853



871
904



872
776



873
840



874
862



875
912



876
873



877
922



878
933



879
968



880
799



881
869



882
880



883
929



884
892



885
939



886
924



887
979



888
901



889
945



890
953



891
972



892
956



893
988



894
994



895
1012



896
374



897
575



898
542



899
681



900
604



901
701



902
706



903
802



904
631



905
727



906
735



907
820



908
755



909
831



910
849



911
906



912
657



913
741



914
763



915
828



916
780



917
851



918
864



919
913



920
793



921
872



922
861



923
921



924
887



925
932



926
938



927
973



928
685



929
778



930
759



931
855



932
807



933
866



934
881



935
925



936
815



937
884



938
891



939
942



940
902



941
935



942
949



943
981



944
838



945
895



946
908



947
946



948
916



949
954



950
963



951
986



952
923



953
959



954
969



955
997



956
976



957
990



958
1000



959
1016



960
724



961
784



962
814



963
882



964
829



965
890



966
899



967
944



968
844



969
909



970
905



971
957



972
920



973
951



974
964



975
991



976
863



977
911



978
926



979
967



980
934



981
962



982
978



983
995



984
943



985
980



986
970



987
998



988
985



989
1003



990
1005



991
1014



992
876



993
931



994
940



995
971



996
952



997
977



998
982



999
1001



1000
958



1001
983



1002
993



1003
1008



1004
987



1005
1002



1006
1010



1007
1019



1008
966



1009
996



1010
989



1011
1006



1012
999



1013
1013



1014
1009



1015
1018



1016
1004



1017
1011



1018
1015



1019
1020



1020
1017



1021
1021



1022
1022



1023
1023










Sequence Z2, having a sequence length of 512:

    • [0, 1, 4, 9, 2, 11, 7, 23, 3, 14, 17, 27, 10, 31, 34, 66, 5, 16, 12, 29, 19, 37, 45, 71, 21, 48, 39, 79, 54, 86, 92, 145, 6, 15, 20, 40, 24, 47, 44, 82, 28, 52, 59, 89, 63, 99, 103, 152, 33, 56, 68, 102, 72, 110, 116, 163, 78, 118, 126, 176, 134, 182, 196, 263, 8, 22, 25, 50, 32, 55, 62, 96, 35, 70, 57, 104, 75, 113, 124, 170, 41, 65, 76, 117, 85, 120, 132, 181, 93, 135, 143, 191, 153, 206, 215, 284, 49, 81, 90, 129, 100, 137, 146, 202, 106, 148, 162, 214, 174, 221, 234, 298, 119, 168, 177, 228, 186, 236, 247, 308, 201, 252, 262, 322, 273, 330, 349, 406, 13, 26, 38, 64, 30, 74, 69, 121, 43, 77, 84, 130, 91, 140, 142, 197, 53, 88, 95, 138, 101, 150, 161, 210, 114, 160, 169, 220, 180, 230, 242, 307, 58, 98, 111, 159, 108, 164, 172, 229, 128, 179, 187, 237, 199, 251, 259, 318, 133, 189, 203, 254, 213, 272, 279, 332, 226, 285, 289, 343, 303, 360, 368, 423, 61, 109, 123, 178, 131, 188, 195, 253, 144, 192, 205, 269, 216, 274, 286, 345, 154, 211, 225, 281, 235, 293, 300, 352, 245, 306, 314, 361, 327, 379, 388, 434, 171, 231, 239, 295, 255, 309, 316, 373, 268, 323, 331, 385, 346, 391, 398, 444, 275, 334, 350, 393, 359, 404, 412, 449, 367, 413, 421, 455, 431, 464, 473, 493, 18, 36, 42, 80, 46, 87, 94, 147, 51, 97, 105, 155, 112, 167, 175, 246, 60, 107, 115, 173, 127, 183, 185, 248, 136, 190, 200, 261, 212, 271, 276, 339, 67, 122, 125, 184, 139, 194, 204, 270, 151, 209, 217, 277, 224, 294, 296, 354, 158, 223, 232, 291, 241, 302, 312, 362, 257, 319, 324, 374, 335, 384, 395, 439, 73, 141, 149, 207, 157, 219, 227, 287, 166, 233, 238, 305, 249, 310, 321, 377, 198, 244, 256, 320, 264, 325, 336, 386, 283, 337, 347, 392, 358, 405, 411, 451, 218, 266, 278, 329, 290, 344, 355, 399, 297, 348, 363, 409, 375, 416, 426, 458, 315, 369, 378, 422, 387, 428, 418, 468, 396, 437, 445, 462, 448, 477, 481, 496, 83, 156, 165, 240, 193, 250, 258, 317, 208, 260, 267, 333, 282, 340, 353, 401, 222, 280, 288, 338, 301, 351, 365, 407, 311, 370, 371, 415, 382, 425, 430, 463, 243, 299, 292, 356, 313, 366, 376, 419, 328, 381, 389, 429, 397, 433, 441, 470, 342, 390, 402, 438, 408, 446, 453, 475, 417, 450, 459, 484, 465, 486, 487, 501, 265, 304, 326, 380, 341, 383, 394, 435, 357, 403, 400, 443, 414, 447, 454, 479, 364, 410, 420, 457, 427, 452, 467, 482, 436, 469, 460, 488, 474, 490, 495, 504, 372, 424, 432, 461, 440, 466, 471, 489, 442, 472, 480, 494, 476, 491, 499, 507, 456, 483, 478, 497, 485, 500, 498, 506, 492, 502, 503, 508, 505, 509, 510, 511]












TABLE Z2, having a sequence length of 512:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
4



3
9



4
2



5
11



6
7



7
23



8
3



9
14



10
17



11
27



12
10



13
31



14
34



15
66



16
5



17
16



18
12



19
29



20
19



21
37



22
45



23
71



24
21



25
48



26
39



27
79



28
54



29
86



30
92



31
145



32
6



33
15



34
20



35
40



36
24



37
47



38
44



39
82



40
28



41
52



42
59



43
89



44
63



45
99



46
103



47
152



48
33



49
56



50
68



51
102



52
72



53
110



54
116



55
163



56
78



57
118



58
126



59
176



60
134



61
182



62
196



63
263



64
8



65
22



66
25



67
50



68
32



69
55



70
62



71
96



72
35



73
70



74
57



75
104



76
75



77
113



78
124



79
170



80
41



81
65



82
76



83
117



84
85



85
120



86
132



87
181



88
93



89
135



90
143



91
191



92
153



93
206



94
215



95
284



96
49



97
81



98
90



99
129



100
100



101
137



102
146



103
202



104
106



105
148



106
162



107
214



108
174



109
221



110
234



111
298



112
119



113
168



114
177



115
228



116
186



117
236



118
247



119
308



120
201



121
252



122
262



123
322



124
273



125
330



126
349



127
406



128
13



129
26



130
38



131
64



132
30



133
74



134
69



135
121



136
43



137
77



138
84



139
130



140
91



141
140



142
142



143
197



144
53



145
88



146
95



147
138



148
101



149
150



150
161



151
210



152
114



153
160



154
169



155
220



156
180



157
230



158
242



159
307



160
58



161
98



162
111



163
159



164
108



165
164



166
172



167
229



168
128



169
179



170
187



171
237



172
199



173
251



174
259



175
318



176
133



177
189



178
203



179
254



180
213



181
272



182
279



183
332



184
226



185
285



186
289



187
343



188
303



189
360



190
368



191
423



192
61



193
109



194
123



195
178



196
131



197
188



198
195



199
253



200
144



201
192



202
205



203
269



204
216



205
274



206
286



207
345



208
154



209
211



210
225



211
281



212
235



213
293



214
300



215
352



216
245



217
306



218
314



219
361



220
327



221
379



222
388



223
434



224
171



225
231



226
239



227
295



228
255



229
309



230
316



231
373



232
268



233
323



234
331



235
385



236
346



237
391



238
398



239
444



240
275



241
334



242
350



243
393



244
359



245
404



246
412



247
449



248
367



249
413



250
421



251
455



252
431



253
464



254
473



255
493



256
18



257
36



258
42



259
80



260
46



261
87



262
94



263
147



264
51



265
97



266
105



267
155



268
112



269
167



270
175



271
246



272
60



273
107



274
115



275
173



276
127



277
183



278
185



279
248



280
136



281
190



282
200



283
261



284
212



285
271



286
276



287
339



288
67



289
122



290
125



291
184



292
139



293
194



294
204



295
270



296
151



297
209



298
217



299
277



300
224



301
294



302
296



303
354



304
158



305
223



306
232



307
291



308
241



309
302



310
312



311
362



312
257



313
319



314
324



315
374



316
335



317
384



318
395



319
439



320
73



321
141



322
149



323
207



324
157



325
219



326
227



327
287



328
166



329
233



330
238



331
305



332
249



333
310



334
321



335
377



336
198



337
244



338
256



339
320



340
264



341
325



342
336



343
386



344
283



345
337



346
347



347
392



348
358



349
405



350
411



351
451



352
218



353
266



354
278



355
329



356
290



357
344



358
355



359
399



360
297



361
348



362
363



363
409



364
375



365
416



366
426



367
458



368
315



369
369



370
378



371
422



372
387



373
428



374
418



375
468



376
396



377
437



378
445



379
462



380
448



381
477



382
481



383
496



384
83



385
156



386
165



387
240



388
193



389
250



390
258



391
317



392
208



393
260



394
267



395
333



396
282



397
340



398
353



399
401



400
222



401
280



402
288



403
338



404
301



405
351



406
365



407
407



408
311



409
370



410
371



411
415



412
382



413
425



414
430



415
463



416
243



417
299



418
292



419
356



420
313



421
366



422
376



423
419



424
328



425
381



426
389



427
429



428
397



429
433



430
441



431
470



432
342



433
390



434
402



435
438



436
408



437
446



438
453



439
475



440
417



441
450



442
459



443
484



444
465



445
486



446
487



447
501



448
265



449
304



450
326



451
380



452
341



453
383



454
394



455
435



456
357



457
403



458
400



459
443



460
414



461
447



462
454



463
479



464
364



465
410



466
420



467
457



468
427



469
452



470
467



471
482



472
436



473
469



474
460



475
488



476
474



477
490



478
495



479
504



480
372



481
424



482
432



483
461



484
440



485
466



486
471



487
489



488
442



489
472



490
480



491
494



492
476



493
491



494
499



495
507



496
456



497
483



498
478



499
497



500
485



501
500



502
498



503
506



504
492



505
502



506
503



507
508



508
505



509
509



510
510



511
511










Sequence Z3, having a sequence length of 256:

    • [0, 1, 4, 9, 2, 11, 7, 22, 3, 14, 17, 26, 10, 30, 33, 60, 5, 16, 12, 28, 18, 35, 42, 64, 20, 44, 37, 71, 49, 76, 81, 122, 6, 15, 19, 38, 23, 43, 41, 73, 27, 47, 54, 78, 57, 86, 90, 126, 32, 51, 61, 89, 65, 95, 99, 133, 70, 101, 107, 141, 114, 147, 155, 192, 8, 21, 24, 46, 31, 50, 56, 84, 34, 63, 52, 91, 67, 97, 106, 137, 39, 59, 68, 100, 75, 103, 112, 146, 82, 115, 120, 152, 127, 162, 167, 201, 45, 72, 79, 109, 87, 116, 123, 159, 92, 124, 132, 166, 140, 170, 177, 207, 102, 135, 142, 173, 148, 179, 184, 212, 158, 186, 191, 217, 196, 220, 227, 243, 13, 25, 36, 58, 29, 66, 62, 104, 40, 69, 74, 110, 80, 118, 119, 156, 48, 77, 83, 117, 88, 125, 131, 163, 98, 130, 136, 169, 145, 175, 182, 211, 53, 85, 96, 129, 93, 134, 139, 174, 108, 144, 149, 180, 157, 185, 190, 216, 113, 151, 160, 188, 165, 195, 199, 222, 172, 202, 204, 224, 209, 231, 234, 247, 55, 94, 105, 143, 111, 150, 154, 187, 121, 153, 161, 194, 168, 197, 203, 225, 128, 164, 171, 200, 178, 205, 208, 229, 183, 210, 214, 232, 219, 236, 238, 249, 138, 176, 181, 206, 189, 213, 215, 235, 193, 218, 221, 237, 226, 239, 241, 250, 198, 223, 228, 240, 230, 242, 244, 251, 233, 245, 246, 252, 248, 253, 254, 255]












TABLE Z3, having a sequence length of 256:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
4



3
9



4
2



5
11



6
7



7
22



8
3



9
14



10
17



11
26



12
10



13
30



14
33



15
60



16
5



17
16



18
12



19
28



20
18



21
35



22
42



23
64



24
20



25
44



26
37



27
71



28
49



29
76



30
81



31
122



32
6



33
15



34
19



35
38



36
23



37
43



38
41



39
73



40
27



41
47



42
54



43
78



44
57



45
86



46
90



47
126



48
32



49
51



50
61



51
89



52
65



53
95



54
99



55
133



56
70



57
101



58
107



59
141



60
114



61
147



62
155



63
192



64
8



65
21



66
24



67
46



68
31



69
50



70
56



71
84



72
34



73
63



74
52



75
91



76
67



77
97



78
106



79
137



80
39



81
59



82
68



83
100



84
75



85
103



86
112



87
146



88
82



89
115



90
120



91
152



92
127



93
162



94
167



95
201



96
45



97
72



98
79



99
109



100
87



101
116



102
123



103
159



104
92



105
124



106
132



107
166



108
140



109
170



110
177



111
207



112
102



113
135



114
142



115
173



116
148



117
179



118
184



119
212



120
158



121
186



122
191



123
217



124
196



125
220



126
227



127
243



128
13



129
25



130
36



131
58



132
29



133
66



134
62



135
104



136
40



137
69



138
74



139
110



140
80



141
118



142
119



143
156



144
48



145
77



146
83



147
117



148
88



149
125



150
131



151
163



152
98



153
130



154
136



155
169



156
145



157
175



158
182



159
211



160
53



161
85



162
96



163
129



164
93



165
134



166
139



167
174



168
108



169
144



170
149



171
180



172
157



173
185



174
190



175
216



176
113



177
151



178
160



179
188



180
165



181
195



182
199



183
222



184
172



185
202



186
204



187
224



188
209



189
231



190
234



191
247



192
55



193
94



194
105



195
143



196
111



197
150



198
154



199
187



200
121



201
153



202
161



203
194



204
168



205
197



206
203



207
225



208
128



209
164



210
171



211
200



212
178



213
205



214
208



215
229



216
183



217
210



218
214



219
232



220
219



221
236



222
238



223
249



224
138



225
176



226
181



227
206



228
189



229
213



230
215



231
235



232
193



233
218



234
221



235
237



236
226



237
239



238
241



239
250



240
198



241
223



242
228



243
240



244
230



245
242



246
244



247
251



248
233



249
245



250
246



251
252



252
248



253
253



254
254



255
255










Sequence Z4, having a sequence length of 128:

    • [0, 1, 4, 9, 2, 11, 7, 21, 3, 13, 16, 24, 10, 27, 30, 51, 5, 15, 12, 26, 17, 32, 37, 54, 19, 39, 33, 59, 43, 63, 66, 90, 6, 14, 18, 34, 22, 38, 36, 61, 25, 42, 47, 64, 49, 69, 72, 93, 29, 45, 52, 71, 55, 75, 77, 96, 58, 79, 83, 100, 86, 103, 106, 119, 8, 20, 23, 41, 28, 44, 48, 68, 31, 53, 46, 73, 56, 76, 82, 98, 35, 50, 57, 78, 62, 81, 85, 102, 67, 87, 89, 105, 94, 109, 111, 121, 40, 60, 65, 84, 70, 88, 91, 108, 74, 92, 95, 110, 99, 112, 114, 122, 80, 97, 101, 113, 104, 115, 116, 123, 107, 117, 118, 124, 120, 125, 126, 127]












Table Z4, having a sequence length of 128:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
4



3
9



4
2



5
11



6
7



7
21



8
3



9
13



10
16



11
24



12
10



13
27



14
30



15
51



16
5



17
15



18
12



19
26



20
17



21
32



22
37



23
54



24
19



25
39



26
33



27
59



28
43



29
63



30
66



31
90



32
6



33
14



34
18



35
34



36
22



37
38



38
36



39
61



40
25



41
42



42
47



43
64



44
49



45
69



46
72



47
93



48
29



49
45



50
52



51
71



52
55



53
75



54
77



55
96



56
58



57
79



58
83



59
100



60
86



61
103



62
106



63
119



64
8



65
20



66
23



67
41



68
28



69
44



70
48



71
68



72
31



73
53



74
46



75
73



76
56



77
76



78
82



79
98



80
35



81
50



82
57



83
78



84
62



85
81



86
85



87
102



88
67



89
87



90
89



91
105



92
94



93
109



94
111



95
121



96
40



97
60



98
65



99
84



100
70



101
88



102
91



103
108



104
74



105
92



106
95



107
110



108
99



109
112



110
114



111
122



112
80



113
97



114
101



115
113



116
104



117
115



118
116



119
123



120
107



121
117



122
118



123
124



124
120



125
125



126
126



127
127










Sequence Z5, having a sequence length of 64:

    • [0, 1, 4, 8, 2, 10, 7, 19, 3, 12, 15, 21, 9, 24, 26, 39, 5, 14, 11, 23, 16, 27, 31, 41, 18, 33, 28, 44, 35, 46, 48, 57, 6, 13, 17, 29, 20, 32, 30, 45, 22, 34, 37, 47, 38, 49, 51, 58, 25, 36, 40, 50, 42, 52, 53, 59, 43, 54, 55, 60, 56, 61, 62, 63]












TABLE Z5, having a sequence length of 64:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
4



3
8



4
2



5
10



6
7



7
19



8
3



9
12



10
15



11
21



12
9



13
24



14
26



15
39



16
5



17
14



18
11



19
23



20
16



21
27



22
31



23
41



24
18



25
33



26
28



27
44



28
35



29
46



30
48



31
57



32
6



33
13



34
17



35
29



36
20



37
32



38
30



39
45



40
22



41
34



42
37



43
47



44
38



45
49



46
51



47
58



48
25



49
36



50
40



51
50



52
42



53
52



54
53



55
59



56
43



57
54



58
55



59
60



60
56



61
61



62
62



63
63










Second group of sequences (obtained by using a criterion that comprehensively considers performance obtained by List (list) whose sizes are respectively 1, 2, 4, 8, and 16, and preferentially considers performance of Lists 1 and 16).


Sequence Q6, having a sequence length of 1024:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 256, 36, 24, 20, 65, 34, 7, 129, 66, 512, 11, 40, 68, 13, 19, 130, 48, 14, 72, 257, 21, 132, 35, 258, 26, 513, 80, 37, 25, 22, 136, 38, 260, 96, 514, 264, 67, 41, 144, 28, 69, 42, 516, 49, 74, 272, 160, 520, 288, 528, 70, 131, 544, 192, 44, 81, 50, 73, 133, 15, 52, 320, 23, 134, 76, 82, 56, 384, 137, 97, 27, 39, 259, 84, 138, 145, 261, 29, 43, 98, 515, 88, 140, 30, 146, 71, 262, 265, 161, 576, 45, 100, 640, 51, 148, 46, 75, 266, 273, 517, 104, 162, 53, 193, 152, 77, 164, 768, 268, 274, 518, 54, 83, 57, 521, 112, 135, 78, 289, 194, 85, 276, 522, 58, 168, 139, 99, 86, 60, 280, 89, 290, 529, 524, 196, 141, 101, 147, 176, 142, 530, 31, 292, 200, 263, 90, 149, 321, 322, 102, 545, 105, 532, 92, 47, 296, 163, 150, 546, 208, 385, 267, 304, 324, 153, 165, 536, 386, 106, 55, 328, 577, 548, 113, 154, 79, 224, 108, 269, 166, 578, 519, 552, 195, 270, 641, 523, 580, 560, 275, 59, 169, 156, 291, 277, 114, 87, 197, 116, 170, 61, 531, 525, 642, 281, 278, 526, 177, 293, 388, 91, 584, 769, 198, 172, 120, 201, 336, 62, 282, 143, 103, 178, 294, 93, 644, 202, 592, 323, 392, 297, 151, 209, 284, 180, 107, 94, 204, 770, 648, 298, 352, 533, 325, 608, 155, 210, 400, 305, 547, 300, 109, 184, 534, 772, 326, 656, 115, 167, 157, 537, 225, 306, 329, 110, 117, 212, 171, 330, 226, 549, 776, 538, 387, 308, 216, 416, 672, 337, 158, 271, 118, 279, 550, 332, 579, 540, 389, 173, 121, 553, 199, 784, 179, 228, 338, 312, 704, 390, 122, 554, 581, 393, 283, 174, 203, 340, 448, 561, 353, 394, 181, 527, 582, 556, 63, 295, 285, 232, 124, 643, 585, 562, 205, 182, 286, 299, 354, 211, 401, 185, 396, 344, 586, 645, 593, 535, 240, 206, 95, 327, 564, 800, 402, 356, 307, 301, 417, 186, 404, 213, 418, 539, 568, 594, 649, 771, 227, 832, 588, 646, 302, 111, 360, 214, 551, 609, 896, 188, 309, 449, 331, 217, 408, 229, 541, 159, 420, 596, 650, 773, 310, 333, 119, 339, 218, 368, 657, 230, 391, 542, 610, 233, 313, 334, 774, 658, 612, 175, 123, 314, 555, 600, 583, 341, 450, 652, 220, 557, 424, 395, 777, 673, 355, 287, 183, 234, 125, 241, 563, 660, 558, 616, 778, 674, 316, 342, 345, 397, 452, 432, 207, 785, 403, 357, 187, 587, 565, 664, 624, 780, 236, 126, 242, 398, 705, 346, 456, 358, 405, 303, 569, 595, 244, 786, 189, 676, 589, 566, 647, 361, 706, 215, 348, 419, 406, 464, 801, 590, 409, 680, 788, 362, 570, 597, 572, 311, 708, 219, 598, 601, 651, 611, 410, 802, 421, 792, 231, 602, 653, 248, 688, 369, 190, 480, 335, 364, 613, 659, 654, 422, 315, 221, 370, 425, 235, 451, 412, 343, 372, 317, 614, 775, 222, 543, 426, 453, 237, 559, 833, 804, 712, 834, 661, 808, 779, 617, 604, 433, 720, 816, 836, 347, 897, 243, 662, 454, 318, 675, 376, 567, 618, 665, 736, 898, 840, 781, 428, 625, 238, 359, 458, 399, 245, 434, 677, 457, 591, 349, 127, 666, 787, 678, 620, 782, 626, 571, 191, 407, 350, 436, 465, 246, 460, 363, 681, 599, 249, 411, 668, 707, 573, 789, 803, 790, 682, 365, 440, 628, 709, 374, 423, 466, 250, 371, 689, 793, 481, 413, 603, 574, 366, 468, 655, 900, 805, 429, 615, 710, 252, 373, 848, 684, 713, 605, 690, 632, 482, 794, 806, 427, 414, 663, 835, 904, 809, 714, 619, 796, 472, 223, 455, 692, 721, 837, 716, 864, 810, 606, 912, 722, 696, 377, 817, 435, 812, 319, 484, 430, 621, 838, 667, 239, 461, 378, 459, 627, 622, 437, 488, 380, 818, 496, 669, 679, 724, 841, 629, 351, 467, 438, 737, 251, 462, 442, 441, 469, 247, 683, 842, 738, 899, 670, 783, 849, 820, 728, 928, 791, 367, 901, 630, 685, 844, 633, 711, 253, 691, 824, 902, 686, 740, 850, 375, 444, 470, 483, 415, 485, 905, 795, 473, 634, 744, 852, 960, 865, 693, 797, 906, 715, 807, 474, 636, 694, 254, 717, 575, 811, 697, 866, 798, 379, 431, 913, 607, 489, 723, 486, 908, 718, 813, 476, 856, 839, 725, 698, 914, 752, 868, 819, 814, 439, 929, 490, 623, 671, 739, 916, 872, 381, 930, 497, 821, 463, 726, 961, 843, 492, 631, 729, 700, 443, 741, 845, 920, 382, 822, 851, 730, 498, 880, 742, 445, 903, 687, 825, 932, 471, 635, 846, 500, 745, 962, 826, 732, 446, 936, 255, 853, 475, 753, 695, 867, 637, 907, 487, 746, 828, 854, 504, 799, 909, 857, 964, 719, 477, 915, 699, 493, 748, 944, 858, 873, 638, 968, 478, 383, 754, 869, 491, 910, 815, 917, 727, 870, 701, 931, 499, 860, 756, 922, 731, 976, 918, 874, 823, 502, 933, 743, 760, 881, 494, 702, 921, 827, 876, 501, 847, 992, 934, 447, 733, 882, 937, 963, 747, 505, 855, 924, 734, 829, 965, 884, 938, 506, 749, 945, 966, 755, 859, 940, 830, 911, 871, 639, 888, 479, 946, 750, 969, 508, 861, 757, 970, 919, 875, 862, 758, 948, 977, 923, 972, 761, 877, 952, 495, 703, 935, 978, 883, 762, 503, 925, 878, 735, 993, 885, 939, 994, 980, 926, 764, 941, 967, 886, 831, 947, 507, 889, 984, 751, 942, 996, 971, 890, 509, 949, 973, 1000, 892, 950, 863, 759, 1008, 510, 979, 953, 763, 974, 954, 879, 981, 982, 927, 995, 765, 956, 887, 985, 997, 986, 943, 891, 998, 766, 511, 988, 1001, 951, 1002, 893, 975, 894, 1009, 955, 1004, 1010, 957, 983, 958, 987, 1012, 999, 1016, 767, 989, 1003, 990, 1005, 959, 1011, 1013, 895, 1006, 1014, 1017, 1018, 991, 1020, 1007, 1015, 1019, 1021, 1022, 1023]









TABLE Q6







having a sequence length of 1024:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
64



10
9



11
6



12
17



13
10



14
18



15
128



16
12



17
33



18
256



19
36



20
24



21
20



22
65



23
34



24
7



25
129



26
66



27
512



28
11



29
40



30
68



31
13



32
19



33
130



34
48



35
14



36
72



37
257



38
21



39
132



40
35



41
258



42
26



43
513



44
80



45
37



46
25



47
22



48
136



49
38



50
260



51
96



52
514



53
264



54
67



55
41



56
144



57
28



58
69



59
42



60
516



61
49



62
74



63
272



64
160



65
520



66
288



67
528



68
70



69
131



70
544



71
192



72
44



73
81



74
50



75
73



76
133



77
15



78
52



79
320



80
23



81
134



82
76



83
82



84
56



85
384



86
137



87
97



88
27



89
39



90
259



91
84



92
138



93
145



94
261



95
29



96
43



97
98



98
515



99
88



100
140



101
30



102
146



103
71



104
262



105
265



106
161



107
576



108
45



109
100



110
640



111
51



112
148



113
46



114
75



115
266



116
273



117
517



118
104



119
162



120
53



121
193



122
152



123
77



124
164



125
768



126
268



127
274



128
518



129
54



130
83



131
57



132
521



133
112



134
135



135
78



136
289



137
194



138
85



139
276



140
522



141
58



142
168



143
139



144
99



145
86



146
60



147
280



148
89



149
290



150
529



151
524



152
196



153
141



154
101



155
147



156
176



157
142



158
530



159
31



160
292



161
200



162
263



163
90



164
149



165
321



166
322



167
102



168
545



169
105



170
532



171
92



172
47



173
296



174
163



175
150



176
546



177
208



178
385



179
267



180
304



181
324



182
153



183
165



184
536



185
386



186
106



187
55



188
328



189
577



190
548



191
113



192
154



193
79



194
224



195
108



196
269



197
166



198
578



199
519



200
552



201
195



202
270



203
641



204
523



205
580



206
560



207
275



208
59



209
169



210
156



211
291



212
277



213
114



214
87



215
197



216
116



217
170



218
61



219
531



220
525



221
642



222
281



223
278



224
526



225
177



226
293



227
388



228
91



229
584



230
769



231
198



232
172



233
120



234
201



235
336



236
62



237
282



238
143



239
103



240
178



241
294



242
93



243
644



244
202



245
592



246
323



247
392



248
297



249
151



250
209



251
284



252
180



253
107



254
94



255
204



256
770



257
648



258
298



259
352



260
533



261
325



262
608



263
155



264
210



265
400



266
305



267
547



268
300



269
109



270
184



271
534



272
772



273
326



274
656



275
115



276
167



277
157



278
537



279
225



280
306



281
329



282
110



283
117



284
212



285
171



286
330



287
226



288
549



289
776



290
538



291
387



292
308



293
216



294
416



295
672



296
337



297
158



298
271



299
118



300
279



301
550



302
332



303
579



304
540



305
389



306
173



307
121



308
553



309
199



310
784



311
179



312
228



313
338



314
312



315
704



316
390



317
122



318
554



319
581



320
393



321
283



322
174



323
203



324
340



325
448



326
561



327
353



328
394



329
181



330
527



331
582



332
556



333
63



334
295



335
285



336
232



337
124



338
643



339
585



340
562



341
205



342
182



343
286



344
299



345
354



346
211



347
401



348
185



349
396



350
344



351
586



352
645



353
593



354
535



355
240



356
206



357
95



358
327



359
564



360
800



361
402



362
356



363
307



364
301



365
417



366
186



367
404



368
213



369
418



370
539



371
568



372
594



373
649



374
771



375
227



376
832



377
588



378
646



379
302



380
111



381
360



382
214



383
551



384
609



385
896



386
188



387
309



388
449



389
331



390
217



391
408



392
229



393
541



394
159



395
420



396
596



397
650



398
773



399
310



400
333



401
119



402
339



403
218



404
368



405
657



406
230



407
391



408
542



409
610



410
233



411
313



412
334



413
774



414
658



415
612



416
175



417
123



418
314



419
555



420
600



421
583



422
341



423
450



424
652



425
220



426
557



427
424



428
395



429
777



430
673



431
355



432
287



433
183



434
234



435
125



436
241



437
563



438
660



439
558



440
616



441
778



442
674



443
316



444
342



445
345



446
397



447
452



448
432



449
207



450
785



451
403



452
357



453
187



454
587



455
565



456
664



457
624



458
780



459
236



460
126



461
242



462
398



463
705



464
346



465
456



466
358



467
405



468
303



469
569



470
595



471
244



472
786



473
189



474
676



475
589



476
566



477
647



478
361



479
706



480
215



481
348



482
419



483
406



484
464



485
801



486
590



487
409



488
680



489
788



490
362



491
570



492
597



493
572



494
311



495
708



496
219



497
598



498
601



499
651



500
611



501
410



502
802



503
421



504
792



505
231



506
602



507
653



508
248



509
688



510
369



511
190



512
480



513
335



514
364



515
613



516
659



517
654



518
422



519
315



520
221



521
370



522
425



523
235



524
451



525
412



526
343



527
372



528
317



529
614



530
775



531
222



532
543



533
426



534
453



535
237



536
559



537
833



538
804



539
712



540
834



541
661



542
808



543
779



544
617



545
604



546
433



547
720



548
816



549
836



550
347



551
897



552
243



553
662



554
454



555
318



556
675



557
376



558
567



559
618



560
665



561
736



562
898



563
840



564
781



565
428



566
625



567
238



568
359



569
458



570
399



571
245



572
434



573
677



574
457



575
591



576
349



577
127



578
666



579
787



580
678



581
620



582
782



583
626



584
571



585
191



586
407



587
350



588
436



589
465



590
246



591
460



592
363



593
681



594
599



595
249



596
411



597
668



598
707



599
573



600
789



601
803



602
790



603
682



604
365



605
440



606
628



607
709



608
374



609
423



610
466



611
250



612
371



613
689



614
793



615
481



616
413



617
603



618
574



619
366



620
468



621
655



622
900



623
805



624
429



625
615



626
710



627
252



628
373



629
848



630
684



631
713



632
605



633
690



634
632



635
482



636
794



637
806



638
427



639
414



640
663



641
835



642
904



643
809



644
714



645
619



646
796



647
472



648
223



649
455



650
692



651
721



652
837



653
716



654
864



655
810



656
606



657
912



658
722



659
696



660
377



661
817



662
435



663
812



664
319



665
484



666
430



667
621



668
838



669
667



670
239



671
461



672
378



673
459



674
627



675
622



676
437



677
488



678
380



679
818



680
496



681
669



682
679



683
724



684
841



685
629



686
351



687
467



688
438



689
737



690
251



691
462



692
442



693
441



694
469



695
247



696
683



697
842



698
738



699
899



700
670



701
783



702
849



703
820



704
728



705
928



706
791



707
367



708
901



709
630



710
685



711
844



712
633



713
711



714
253



715
691



716
824



717
902



718
686



719
740



720
850



721
375



722
444



723
470



724
483



725
415



726
485



727
905



728
795



729
473



730
634



731
744



732
852



733
960



734
865



735
693



736
797



737
906



738
715



739
807



740
474



741
636



742
694



743
254



744
717



745
575



746
811



747
697



748
866



749
798



750
379



751
431



752
913



753
607



754
489



755
723



756
486



757
908



758
718



759
813



760
476



761
856



762
839



763
725



764
698



765
914



766
752



767
868



768
819



769
814



770
439



771
929



772
490



773
623



774
671



775
739



776
916



777
872



778
381



779
930



780
497



781
821



782
463



783
726



784
961



785
843



786
492



787
631



788
729



789
700



790
443



791
741



792
845



793
920



794
382



795
822



796
851



797
730



798
498



799
880



800
742



801
445



802
903



803
687



804
825



805
932



806
471



807
635



808
846



809
500



810
745



811
962



812
826



813
732



814
446



815
936



816
255



817
853



818
475



819
753



820
695



821
867



822
637



823
907



824
487



825
746



826
828



827
854



828
504



829
799



830
909



831
857



832
964



833
719



834
477



835
915



836
699



837
493



838
748



839
944



840
858



841
873



842
638



843
968



844
478



845
383



846
754



847
869



848
491



849
910



850
815



851
917



852
727



853
870



854
701



855
931



856
499



857
860



858
756



859
922



860
731



861
976



862
918



863
874



864
823



865
502



866
933



867
743



868
760



869
881



870
494



871
702



872
921



873
827



874
876



875
501



876
847



877
992



878
934



879
447



880
733



881
882



882
937



883
963



884
747



885
505



886
855



887
924



888
734



889
829



890
965



891
884



892
938



893
506



894
749



895
945



896
966



897
755



898
859



899
940



900
830



901
911



902
871



903
639



904
888



905
479



906
946



907
750



908
969



909
508



910
861



911
757



912
970



913
919



914
875



915
862



916
758



917
948



918
977



919
923



920
972



921
761



922
877



923
952



924
495



925
703



926
935



927
978



928
883



929
762



930
503



931
925



932
878



933
735



934
993



935
885



936
939



937
994



938
980



939
926



940
764



941
941



942
967



943
886



944
831



945
947



946
507



947
889



948
984



949
751



950
842



951
996



952
971



953
890



954
509



955
949



956
973



957
1000



958
892



959
950



960
863



961
759



962
1008



963
510



964
979



965
953



966
763



967
974



968
954



969
879



970
981



971
982



972
927



973
995



974
765



975
956



976
887



977
985



978
997



979
986



980
943



981
891



982
998



983
766



984
511



985
988



986
1001



987
951



988
1002



989
893



990
975



991
894



992
1009



993
955



994
1004



995
1010



996
957



997
983



998
958



999
987



1000
1012



1001
999



1002
1016



1003
767



1004
989



1005
1003



1006
990



1007
1005



1008
959



1009
1011



1010
1013



1011
895



1012
1006



1013
1014



1014
1017



1015
1018



1016
991



1017
1020



1018
1007



1019
1015



1020
1019



1021
1021



1022
1022



1023
1023










Sequence Q7, having a sequence length of 512:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 256, 36, 24, 20, 65, 34, 7, 129, 66, 11, 40, 68, 13, 19, 130, 48, 14, 72, 257, 21, 132, 35, 258, 26, 80, 37, 25, 22, 136, 38, 260, 96, 264, 67, 41, 144, 28, 69, 42, 49, 74, 272, 160, 288, 70, 131, 192, 44, 81, 50, 73, 133, 15, 52, 320, 23, 134, 76, 82, 56, 384, 137, 97, 27, 39, 259, 84, 138, 145, 261, 29, 43, 98, 88, 140, 30, 146, 71, 262, 265, 161, 45, 100, 51, 148, 46, 75, 266, 273, 104, 162, 53, 193, 152, 77, 164, 268, 274, 54, 83, 57, 112, 135, 78, 289, 194, 85, 276, 58, 168, 139, 99, 86, 60, 280, 89, 290, 196, 141, 101, 147, 176, 142, 31, 292, 200, 263, 90, 149, 321, 322, 102, 105, 92, 47, 296, 163, 150, 208, 385, 267, 304, 324, 153, 165, 386, 106, 55, 328, 113, 154, 79, 224, 108, 269, 166, 195, 270, 275, 59, 169, 156, 291, 277, 114, 87, 197, 116, 170, 61, 281, 278, 177, 293, 388, 91, 198, 172, 120, 201, 336, 62, 282, 143, 103, 178, 294, 93, 202, 323, 392, 297, 151, 209, 284, 180, 107, 94, 204, 298, 352, 325, 155, 210, 400, 305, 300, 109, 184, 326, 115, 167, 157, 225, 306, 329, 110, 117, 212, 171, 330, 226, 387, 308, 216, 416, 337, 158, 271, 118, 279, 332, 389, 173, 121, 199, 179, 228, 338, 312, 390, 122, 393, 283, 174, 203, 340, 448, 353, 394, 181, 63, 295, 285, 232, 124, 205, 182, 286, 299, 354, 211, 401, 185, 396, 344, 240, 206, 95, 327, 402, 356, 307, 301, 417, 186, 404, 213, 418, 227, 302, 111, 360, 214, 188, 309, 449, 331, 217, 408, 229, 159, 420, 310, 333, 119, 339, 218, 368, 230, 391, 233, 313, 334, 175, 123, 314, 341, 450, 220, 424, 395, 355, 287, 183, 234, 125, 241, 316, 342, 345, 397, 452, 432, 207, 403, 357, 187, 236, 126, 242, 398, 346, 456, 358, 405, 303, 244, 189, 361, 215, 348, 419, 406, 464, 409, 362, 311, 219, 410, 421, 231, 248, 369, 190, 480, 335, 364, 422, 315, 221, 370, 425, 235, 451, 412, 343, 372, 317, 222, 426, 453, 237, 433, 347, 243, 454, 318, 376, 428, 238, 359, 458, 399, 245, 434, 457, 349, 127, 191, 407, 350, 436, 465, 246, 460, 363, 249, 411, 365, 440, 374, 423, 466, 250, 371, 481, 413, 366, 468, 429, 252, 373, 482, 427, 414, 472, 223, 455, 377, 435, 319, 484, 430, 239, 461, 378, 459, 437, 488, 380, 496, 351, 467, 438, 251, 462, 442, 441, 469, 247, 367, 253, 375, 444, 470, 483, 415, 485, 473, 474, 254, 379, 431, 489, 486, 476, 439, 490, 381, 497, 463, 492, 443, 382, 498, 445, 471, 500, 446, 255, 475, 487, 504, 477, 493, 478, 383, 491, 499, 502, 494, 501, 447, 505, 506, 479, 508, 495, 503, 507, 509, 510, 511]












Table Q7, having a sequence length of 512:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
64



10
9



11
6



12
17



13
10



14
18



15
128



16
12



17
33



18
256



19
36



20
24



21
20



22
65



23
34



24
7



25
129



26
66



27
11



28
40



29
68



30
13



31
19



32
130



33
48



34
14



35
72



36
257



37
21



38
132



39
35



40
258



41
26



42
80



43
37



44
25



45
22



46
136



47
38



48
260



49
96



50
264



51
67



52
41



53
144



54
28



55
69



56
42



57
49



58
74



59
272



60
160



61
288



62
70



63
131



64
192



65
44



66
81



67
50



68
73



69
133



70
15



71
52



72
320



73
23



74
134



75
76



76
82



77
56



78
384



79
137



80
97



81
27



82
39



83
259



84
84



85
138



86
145



87
261



88
29



89
43



90
98



91
88



92
140



93
30



94
146



95
71



96
262



97
265



98
161



99
45



100
100



101
51



102
148



103
46



104
75



105
266



106
273



107
104



108
162



109
53



110
193



111
152



112
77



113
164



114
268



115
274



116
54



117
83



118
57



119
112



120
135



121
78



122
289



123
194



124
85



125
276



126
58



127
168



128
139



129
99



130
86



131
60



132
280



133
89



134
290



135
196



136
141



137
101



138
147



139
176



140
142



141
31



142
292



143
200



144
263



145
90



146
149



147
321



148
322



149
102



150
105



151
92



152
47



153
296



154
163



155
150



156
208



157
385



158
267



159
304



160
324



161
153



162
165



163
386



164
106



165
55



166
328



167
113



168
154



169
79



170
224



171
108



172
269



173
166



174
195



175
270



176
275



177
59



178
169



179
156



180
291



181
277



182
114



183
87



184
197



185
116



186
170



187
61



188
281



189
278



190
177



191
293



192
388



193
91



194
198



195
172



196
120



197
201



198
336



199
62



200
282



201
143



202
103



203
178



204
294



205
93



206
202



207
323



208
392



209
297



210
151



211
209



212
284



213
180



214
107



215
94



216
204



217
298



218
352



219
325



220
155



221
210



222
400



223
305



224
300



225
109



226
184



227
326



228
115



229
167



230
157



231
225



232
306



233
329



234
110



235
117



236
212



237
171



238
330



239
226



240
387



241
308



242
216



243
416



244
337



245
158



246
271



247
118



248
279



249
332



250
389



251
173



252
121



253
199



254
179



255
228



256
338



257
312



258
390



259
122



260
393



261
283



262
174



263
203



264
340



265
448



266
353



267
394



268
181



269
63



270
295



271
285



272
232



273
124



274
205



275
182



276
286



277
299



278
354



279
211



280
401



281
185



282
396



283
344



284
240



285
206



286
95



287
327



288
402



289
356



290
307



291
301



292
417



293
186



294
404



295
213



296
418



297
227



298
302



299
111



300
360



301
214



302
188



303
309



304
449



305
331



306
217



307
408



308
229



309
159



310
420



311
310



312
333



313
119



314
339



315
218



316
368



317
230



318
391



319
233



320
313



321
334



322
175



323
123



324
314



325
341



326
450



327
220



328
424



329
395



330
355



331
287



332
183



333
234



334
125



335
241



336
316



337
342



338
345



339
397



340
452



341
432



342
207



343
403



344
357



345
187



346
236



347
126



348
242



349
398



350
346



351
456



352
358



353
405



354
303



355
244



356
189



357
361



358
215



359
348



360
419



361
406



362
464



363
409



364
362



365
311



366
219



367
410



368
421



369
231



370
248



371
369



372
190



373
480



374
335



375
364



376
422



377
315



378
221



379
370



380
425



381
235



382
451



383
412



384
343



385
372



386
317



387
222



388
426



389
453



390
237



391
433



392
347



393
243



394
454



395
318



396
376



397
428



398
238



399
359



400
458



401
399



402
245



403
434



404
457



405
349



406
127



407
191



408
407



409
350



410
436



411
465



412
246



413
460



414
363



415
249



416
411



417
365



418
440



419
374



420
423



421
466



422
250



423
371



424
481



425
413



426
366



427
468



428
429



429
252



430
373



431
482



432
427



433
414



434
472



435
223



436
455



437
377



438
435



439
319



440
484



441
430



442
239



443
461



444
378



445
459



446
437



447
488



448
380



449
496



450
351



451
467



452
438



453
251



454
462



455
442



456
441



457
469



458
247



459
367



460
253



461
375



462
444



463
470



464
483



465
415



466
485



467
473



468
474



469
254



470
379



471
431



472
489



473
486



474
476



475
439



476
490



477
381



478
497



479
463



480
492



481
443



482
382



483
498



484
445



485
471



486
500



487
446



488
255



489
475



490
487



491
504



492
477



493
493



494
478



495
383



496
491



497
499



498
502



499
494



500
501



501
447



502
505



503
506



504
479



505
508



506
495



507
503



508
507



509
509



510
510



511
511










Sequence Q8, having a sequence length of 256:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 36, 24, 20, 65, 34, 7, 129, 66, 11, 40, 68, 13, 19, 130, 48, 14, 72, 21, 132, 35, 26, 80, 37, 25, 22, 136, 38, 96, 67, 41, 144, 28, 69, 42, 49, 74, 160, 70, 131, 192, 44, 81, 50, 73, 133, 15, 52, 23, 134, 76, 82, 56, 137, 97, 27, 39, 84, 138, 145, 29, 43, 98, 88, 140, 30, 146, 71, 161, 45, 100, 51, 148, 46, 75, 104, 162, 53, 193, 152, 77, 164, 54, 83, 57, 112, 135, 78, 194, 85, 58, 168, 139, 99, 86, 60, 89, 196, 141, 101, 147, 176, 142, 31, 200, 90, 149, 102, 105, 92, 47, 163, 150, 208, 153, 165, 106, 55, 113, 154, 79, 224, 108, 166, 195, 59, 169, 156, 114, 87, 197, 116, 170, 61, 177, 91, 198, 172, 120, 201, 62, 143, 103, 178, 93, 202, 151, 209, 180, 107, 94, 204, 155, 210, 109, 184, 115, 167, 157, 225, 110, 117, 212, 171, 226, 216, 158, 118, 173, 121, 199, 179, 228, 122, 174, 203, 181, 63, 232, 124, 205, 182, 211, 185, 240, 206, 95, 186, 213, 227, 111, 214, 188, 217, 229, 159, 119, 218, 230, 233, 175, 123, 220, 183, 234, 125, 241, 207, 187, 236, 126, 242, 244, 189, 215, 219, 231, 248, 190, 221, 235, 222, 237, 243, 238, 245, 127, 191, 246, 249, 250, 252, 223, 239, 251, 247, 253, 254, 255]












Table Q8, having a sequence length of 256:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
64



10
9



11
6



12
17



13
10



14
18



15
128



16
12



17
33



18
36



19
24



20
20



21
65



22
34



23
7



24
129



25
66



26
11



27
40



28
68



29
13



30
19



31
130



32
48



33
14



34
72



35
21



36
132



37
35



38
26



39
80



40
37



41
25



42
22



43
136



44
38



45
96



46
67



47
41



48
144



49
28



50
69



51
42



52
49



53
74



54
160



55
70



56
131



57
192



58
44



59
81



60
50



61
73



62
133



63
15



64
52



65
23



66
134



67
76



68
82



69
56



70
137



71
97



72
27



73
39



74
84



75
138



76
145



77
29



78
43



79
98



80
88



81
140



82
30



83
146



84
71



85
161



86
45



87
100



88
51



89
148



90
46



91
75



92
104



93
162



94
53



95
193



96
152



97
77



98
164



99
54



100
83



101
57



102
112



103
135



104
78



105
194



106
85



107
58



108
168



109
139



110
99



111
86



112
60



113
89



114
196



115
141



116
101



117
147



118
176



119
142



120
31



121
200



122
90



123
149



124
102



125
105



126
92



127
47



128
163



129
150



130
208



131
153



132
165



133
106



134
55



135
113



136
154



137
79



138
224



139
108



140
166



141
195



142
59



143
169



144
156



145
114



146
87



147
197



148
116



149
170



150
61



151
177



152
91



153
198



154
172



155
120



156
201



157
62



158
143



159
103



160
178



161
93



162
202



163
151



164
209



165
180



166
107



167
94



168
204



169
155



170
210



171
109



172
184



173
115



174
167



175
157



176
225



177
110



178
117



179
212



180
171



181
226



182
216



183
158



184
118



185
173



186
121



187
199



188
179



189
228



190
122



191
174



192
203



193
181



194
63



195
232



196
124



197
205



198
182



199
211



200
185



201
240



202
206



203
95



204
186



205
213



206
227



207
111



208
214



209
188



210
217



211
229



212
159



213
119



214
218



215
230



216
233



217
175



218
123



219
220



220
183



221
234



222
125



223
241



224
207



225
187



226
236



227
126



228
242



229
244



230
189



231
215



232
219



233
231



234
248



235
190



236
221



237
235



238
222



239
237



240
243



241
238



242
245



243
127



244
191



245
246



246
249



247
250



248
252



249
223



250
239



251
251



252
247



253
253



254
254



255
255










Sequence Q9, having a sequence length of 128:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 12, 33, 36, 24, 20, 65, 34, 7, 66, 11, 40, 68, 13, 19, 48, 14, 72, 21, 35, 26, 80, 37, 25, 22, 38, 96, 67, 41, 28, 69, 42, 49, 74, 70, 44, 81, 50, 73, 15, 52, 23, 76, 82, 56, 97, 27, 39, 84, 29, 43, 98, 88, 30, 71, 45, 100, 51, 46, 75, 104, 53, 77, 54, 83, 57, 112, 78, 85, 58, 99, 86, 60, 89, 101, 31, 90, 102, 105, 92, 47, 106, 55, 113, 79, 108, 59, 114, 87, 116, 61, 91, 120, 62, 103, 93, 107, 94, 109, 115, 110, 117, 118, 121, 122, 63, 124, 95, 111, 119, 123, 125, 126, 127]









TABLE Q9





having a sequence length of 128:























Reliability
Polarized
Reliability
Polarized
Reliability
Polarized
Reliability
Polarized
Reliability


or sequence
channel
or sequence
channel
or sequence
channel
or sequence
channel
or sequence


number of
sequence
number of
sequence
number of
sequence
number of
sequence
number of


reliability
number
reliability
number
reliability
number
reliability
number
reliability





0
0
16
33
32
21
48
70
64


1
1
17
36
33
35
49
44
65


2
2
18
24
34
26
50
81
66


3
4
19
20
35
80
51
50
67


4
8
20
65
36
37
52
73
68


5
16
21
34
37
25
53
15
69


6
32
22
7
38
22
54
52
70


7
3
23
66
39
38
55
23
71


8
5
24
11
40
96
56
76
72


9
64
25
40
41
67
57
82
73


10
9
26
68
42
41
58
56
74


11
6
27
13
43
28
59
97
75


12
17
28
19
44
69
60
27
76


13
10
29
48
45
42
61
39
77


14
18
30
14
46
49
62
84
78


15
12
31
72
47
74
63
29
79


















Polarized
Reliability
Polarized
Reliability
Polarized
Reliability
Polarized



channel
or sequence
channel
or sequence
channel
or sequence
channel



sequence
number of
sequence
number of
sequence
number of
sequence



number
reliability
number
reliability
number
reliability
number






43
80
112
96
55
112
109



98
81
78
97
113
113
115



88
82
85
98
79
114
110



30
83
58
99
108
115
117



71
84
99
100
59
116
118



45
85
86
101
114
117
121



100
86
60
102
87
118
122



51
87
89
103
116
119
63



46
88
101
104
61
120
124



75
89
31
105
91
121
95



104
90
90
106
120
122
111



53
91
102
107
62
123
119



77
92
105
108
103
124
123



54
93
92
109
93
125
125



83
94
47
110
107
126
126



57
95
106
111
94
127
127









Sequence Q10, having a sequence length of 64:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 9, 6, 17, 10, 18, 12, 33, 36, 24, 20, 34, 7, 11, 40, 13, 19, 48, 14, 21, 35, 26, 37, 25, 22, 38, 41, 28, 42, 49, 44, 50, 15, 52, 23, 56, 27, 39, 29, 43, 30, 45, 51, 46, 53, 54, 57, 58, 60, 31, 47, 55, 59, 61, 62, 63]












Table Q10, having a sequence length of 64:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
9



10
6



11
17



12
10



13
18



14
12



15
33



16
36



17
24



18
20



19
34



20
7



21
11



22
40



23
13



24
19



25
48



26
14



27
21



28
35



29
26



30
37



31
25



32
22



33
38



34
41



35
28



36
42



37
49



38
44



39
50



40
15



41
52



42
23



43
56



44
27



45
39



46
29



47
43



48
30



49
45



50
51



51
46



52
53



53
54



54
57



55
58



56
60



57
31



58
47



59
55



60
59



61
61



62
62



63
63










Sequence Z6, having a sequence length of 1024:

    • [0, 1, 2, 7, 3, 8, 11, 24, 4, 10, 13, 28, 16, 31, 35, 77, 5, 12, 14, 32, 21, 38, 47, 80, 20, 46, 42, 88, 57, 95, 101, 159, 6, 17, 23, 40, 19, 45, 49, 89, 29, 55, 59, 96, 72, 108, 113, 172, 34, 61, 74, 111, 78, 120, 129, 187, 84, 131, 141, 208, 146, 218, 236, 333, 9, 22, 26, 54, 30, 58, 68, 103, 36, 75, 62, 114, 82, 123, 135, 193, 44, 73, 83, 130, 91, 138, 145, 214, 99, 148, 163, 228, 171, 242, 254, 357, 51, 87, 97, 144, 109, 154, 167, 239, 118, 169, 186, 253, 195, 269, 282, 380, 133, 191, 213, 275, 216, 283, 299, 401, 233, 307, 317, 417, 337, 435, 460, 577, 15, 25, 33, 69, 39, 76, 81, 134, 48, 86, 92, 143, 100, 153, 157, 238, 56, 93, 102, 155, 112, 164, 175, 249, 122, 182, 192, 263, 210, 277, 297, 394, 64, 106, 119, 174, 124, 183, 197, 276, 142, 209, 217, 285, 232, 306, 322, 416, 156, 225, 240, 311, 252, 329, 342, 433, 270, 348, 366, 453, 386, 473, 511, 585, 71, 121, 137, 201, 152, 215, 231, 309, 161, 234, 244, 323, 255, 341, 356, 449, 177, 250, 264, 346, 284, 368, 382, 480, 293, 390, 403, 496, 425, 520, 531, 648, 194, 279, 287, 375, 312, 392, 406, 505, 336, 410, 434, 523, 459, 535, 567, 670, 355, 436, 461, 552, 471, 571, 590, 695, 508, 595, 611, 690, 627, 714, 743, 816, 18, 37, 41, 90, 50, 94, 104, 162, 53, 105, 115, 179, 126, 196, 202, 298, 63, 116, 127, 207, 139, 212, 223, 300, 147, 222, 237, 321, 251, 335, 343, 432, 66, 136, 149, 211, 160, 226, 241, 334, 173, 248, 258, 344, 268, 364, 379, 468, 180, 266, 280, 363, 292, 387, 399, 494, 314, 411, 418, 519, 443, 528, 555, 664, 79, 165, 166, 246, 181, 261, 273, 358, 188, 281, 286, 389, 302, 400, 412, 513, 235, 296, 313, 402, 324, 422, 444, 526, 350, 445, 464, 550, 481, 576, 587, 686, 259, 327, 345, 431, 362, 452, 466, 568, 381, 478, 490, 592, 514, 604, 619, 707, 404, 510, 521, 612, 527, 628, 608, 721, 557, 660, 672, 750, 678, 778, 794, 845, 85, 178, 185, 291, 227, 305, 316, 407, 247, 320, 328, 428, 349, 446, 462, 570, 265, 347, 361, 451, 367, 467, 483, 586, 391, 487, 501, 596, 525, 616, 639, 725, 294, 365, 369, 482, 395, 503, 518, 609, 427, 522, 533, 638, 565, 624, 666, 751, 448, 546, 572, 662, 588, 676, 688, 770, 605, 693, 692, 790, 722, 801, 814, 879, 325, 388, 423, 524, 447, 534, 554, 649, 465, 574, 569, 673, 591, 671, 691, 782, 484, 589, 610, 687, 620, 694, 723, 806, 647, 729, 740, 818, 760, 834, 844, 905, 512, 615, 635, 724, 665, 726, 756, 824, 677, 754, 772, 848, 786, 837, 870, 924, 680, 780, 798, 856, 809, 875, 865, 930, 828, 885, 893, 946, 909, 954, 963, 984, 27, 43, 52, 98, 60, 117, 128, 199, 65, 132, 140, 204, 151, 220, 224, 330, 67, 150, 158, 219, 170, 260, 271, 354, 184, 278, 290, 370, 304, 393, 408, 532, 70, 168, 176, 267, 190, 288, 301, 383, 200, 308, 318, 419, 332, 426, 439, 536, 206, 326, 340, 437, 359, 455, 476, 558, 371, 469, 491, 584, 493, 599, 618, 745, 107, 189, 198, 303, 205, 319, 331, 421, 229, 339, 351, 454, 377, 475, 486, 575, 245, 353, 372, 470, 396, 492, 497, 594, 420, 498, 506, 617, 545, 632, 656, 753, 262, 384, 409, 500, 415, 515, 529, 625, 440, 544, 559, 645, 581, 667, 675, 773, 457, 566, 583, 674, 606, 685, 709, 787, 634, 712, 730, 807, 741, 822, 842, 903, 110, 203, 221, 338, 243, 352, 378, 477, 257, 373, 397, 499, 424, 507, 517, 621, 274, 405, 414, 516, 438, 541, 553, 640, 456, 560, 578, 669, 597, 681, 700, 774, 295, 430, 442, 556, 474, 573, 580, 682, 488, 593, 603, 696, 630, 710, 718, 803, 509, 613, 633, 715, 650, 735, 742, 820, 659, 747, 764, 836, 789, 854, 871, 925, 315, 463, 479, 598, 495, 607, 626, 713, 539, 631, 644, 738, 653, 744, 758, 833, 547, 651, 658, 755, 683, 763, 783, 852, 704, 788, 797, 860, 813, 880, 888, 933, 561, 689, 698, 775, 719, 791, 800, 867, 731, 810, 825, 884, 838, 894, 907, 949, 766, 819, 846, 897, 858, 911, 916, 961, 868, 921, 929, 966, 940, 974, 983, 1003, 125, 230, 256, 374, 272, 398, 413, 530, 289, 429, 441, 543, 458, 564, 582, 701, 310, 450, 472, 579, 489, 600, 602, 706, 504, 614, 636, 728, 646, 736, 749, 829, 360, 485, 502, 601, 538, 623, 637, 739, 542, 643, 655, 746, 663, 759, 769, 850, 548, 661, 679, 768, 703, 781, 795, 864, 716, 804, 812, 873, 826, 889, 900, 944, 376, 537, 540, 641, 549, 652, 668, 762, 563, 684, 697, 785, 711, 792, 808, 876, 629, 702, 720, 796, 732, 817, 827, 886, 761, 831, 840, 898, 857, 910, 915, 960, 654, 734, 748, 821, 767, 847, 853, 902, 777, 841, 863, 914, 874, 922, 932, 969, 799, 869, 881, 928, 891, 935, 943, 976, 904, 947, 953, 981, 958, 989, 991, 1011, 385, 551, 562, 699, 622, 708, 717, 802, 642, 727, 737, 823, 757, 830, 849, 901, 657, 752, 765, 835, 776, 851, 862, 913, 793, 872, 859, 919, 887, 931, 939, 972, 705, 771, 779, 855, 805, 866, 878, 926, 815, 882, 892, 936, 899, 941, 950, 980, 839, 895, 906, 945, 917, 955, 959, 987, 923, 965, 968, 993, 975, 996, 998, 1008, 733, 784, 811, 883, 832, 890, 896, 942, 843, 908, 912, 952, 920, 956, 967, 990, 861, 918, 927, 964, 938, 970, 971, 997, 948, 977, 979, 999, 985, 1004, 1006, 1016, 877, 934, 937, 973, 951, 978, 982, 1001, 957, 986, 988, 1005, 994, 1007, 1012, 1018, 962, 992, 995, 1009, 1000, 1010, 1013, 1019, 1002, 1014, 1015, 1020, 1017, 1021, 1022, 1023]












Table Z6, having a sequence length of 1024:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
11



7
24



8
4



9
10



10
13



11
28



12
16



13
31



14
35



15
77



16
5



17
12



18
14



19
32



20
21



21
38



22
47



23
80



24
20



25
46



26
42



27
88



28
57



29
95



30
101



31
159



32
6



33
17



34
23



35
40



36
19



37
45



38
49



39
89



40
29



41
55



42
59



43
96



44
72



45
108



46
113



47
172



48
34



49
61



50
74



51
111



52
78



53
120



54
129



55
187



56
84



57
131



58
141



59
208



60
146



61
218



62
236



63
333



64
9



65
22



66
26



67
54



68
30



69
58



70
68



71
103



72
36



73
75



74
62



75
114



76
82



77
123



78
135



79
193



80
44



81
73



82
83



83
130



84
91



85
138



86
145



87
214



88
99



89
148



90
163



91
228



92
171



93
242



94
254



95
357



96
51



97
87



98
97



99
144



100
109



101
154



102
167



103
239



104
118



105
169



106
186



107
253



108
195



109
269



110
282



111
380



112
133



113
191



114
213



115
275



116
216



117
283



118
299



119
401



120
233



121
307



122
317



123
417



124
337



125
435



126
460



127
577



128
15



129
25



130
33



131
69



132
39



133
76



134
81



135
134



136
48



137
86



138
92



139
143



140
100



141
153



142
157



143
238



144
56



145
93



146
102



147
155



148
112



149
164



150
175



151
249



152
122



153
182



154
192



155
263



156
210



157
277



158
297



159
394



160
64



161
106



162
119



163
174



164
124



165
183



166
197



167
276



168
142



169
209



170
217



171
285



172
232



173
306



174
322



175
416



176
156



177
225



178
240



179
311



180
252



181
329



182
342



183
433



184
270



185
348



186
366



187
453



188
386



189
473



190
511



191
585



192
71



193
121



194
137



195
201



196
152



197
215



198
231



199
309



200
161



201
234



202
244



203
323



204
255



205
341



206
356



207
449



208
177



209
250



210
264



211
346



212
284



213
368



214
382



215
480



216
293



217
390



218
403



219
496



220
425



221
520



222
531



223
648



224
194



225
279



226
287



227
375



228
312



229
392



230
406



231
505



232
336



233
410



234
434



235
523



236
459



237
535



238
567



239
670



240
355



241
436



242
461



243
552



244
471



245
571



246
590



247
695



248
508



249
595



250
611



251
690



252
627



253
714



254
743



255
816



256
18



257
37



258
41



259
90



260
50



261
94



262
104



263
162



264
53



265
105



266
115



267
179



268
126



269
196



270
202



271
298



272
63



273
116



274
127



275
207



276
139



277
212



278
223



279
300



280
147



281
222



282
237



283
321



284
251



285
335



286
343



287
432



288
66



289
136



290
149



291
211



292
160



293
226



294
241



295
334



296
173



297
248



298
258



299
344



300
268



301
364



302
379



303
468



304
180



305
266



306
280



307
363



308
292



309
387



310
399



311
494



312
314



313
411



314
418



315
519



316
443



317
528



318
555



319
664



320
79



321
165



322
166



323
246



324
181



325
261



326
273



327
358



328
188



329
281



330
286



331
389



332
302



333
400



334
412



335
513



336
235



337
296



338
313



339
402



340
324



341
422



342
444



343
526



344
350



345
445



346
464



347
550



348
481



349
576



350
587



351
686



352
259



353
327



354
345



355
431



356
362



357
452



358
466



359
568



360
381



361
478



362
490



363
592



364
514



365
604



366
619



367
707



368
404



369
510



370
521



371
612



372
527



373
628



374
608



375
721



376
557



377
660



378
672



379
750



380
678



381
778



382
794



383
845



384
85



385
178



386
185



387
291



388
227



389
305



390
316



391
407



392
247



393
320



394
328



395
428



396
349



397
446



398
462



399
570



400
265



401
347



402
361



403
451



404
367



405
467



406
483



407
586



408
391



409
487



410
501



411
596



412
525



413
616



414
639



415
725



416
294



417
365



418
369



419
482



420
395



421
503



422
518



423
609



424
427



425
522



426
533



427
638



428
565



429
624



430
666



431
751



432
448



433
546



434
572



435
662



436
588



437
676



438
688



439
770



440
605



441
693



442
692



443
790



444
722



445
801



446
814



447
879



448
325



449
388



450
423



451
524



452
447



453
534



454
554



455
649



456
465



457
574



458
569



459
673



460
591



461
671



462
691



463
782



464
484



465
589



466
610



467
687



468
620



469
694



470
723



471
806



472
647



473
729



474
740



475
818



476
760



477
834



478
844



479
905



480
512



481
615



482
635



483
724



484
665



485
726



486
756



487
824



488
677



489
754



490
772



491
848



492
786



493
837



494
870



495
924



496
680



497
780



498
798



499
856



500
809



501
875



502
865



503
930



504
828



505
885



506
893



507
946



508
909



509
954



510
963



511
984



512
27



513
43



514
52



515
98



516
60



517
117



518
128



519
199



520
65



521
132



522
140



523
204



524
151



525
220



526
224



527
330



528
67



529
150



530
158



531
219



532
170



533
260



534
271



535
354



536
184



537
278



538
290



539
370



540
304



541
393



542
408



543
532



544
70



545
168



546
176



547
267



548
190



549
288



550
301



551
383



552
200



553
308



554
318



555
419



556
332



557
426



558
439



559
536



560
206



561
326



562
340



563
437



564
359



565
455



566
476



567
558



568
371



569
469



570
491



571
584



572
493



573
599



574
618



575
745



576
107



577
189



578
198



579
303



580
205



581
319



582
331



583
421



584
229



585
339



586
351



587
454



588
377



589
475



590
486



591
575



592
245



593
353



594
372



595
470



596
396



597
492



598
497



599
594



600
420



601
498



602
506



603
617



604
545



605
632



606
656



607
753



608
262



609
384



610
409



611
500



612
415



613
515



614
529



615
625



616
440



617
544



618
559



619
645



620
581



621
667



622
675



623
773



624
457



625
566



626
583



627
674



628
606



629
685



630
709



631
787



632
634



633
712



634
730



635
807



636
741



637
822



638
842



639
903



640
110



641
203



642
221



643
338



644
243



645
352



646
378



647
477



648
257



649
373



650
397



651
499



652
424



653
507



654
517



655
621



656
274



657
405



658
414



659
516



660
438



661
541



662
553



663
640



664
456



665
560



666
578



667
669



668
597



669
681



670
700



671
774



672
295



673
430



674
442



675
556



676
474



677
573



678
580



679
682



680
488



681
593



682
603



683
696



684
630



685
710



686
718



687
803



688
509



689
613



690
633



691
715



692
650



693
735



694
742



695
820



696
659



697
747



698
764



699
836



700
789



701
854



702
871



703
925



704
315



705
463



706
479



707
598



708
495



709
607



710
626



711
713



712
539



713
631



714
644



715
738



716
653



717
744



718
758



719
833



720
547



721
651



722
658



723
755



724
683



725
763



726
783



727
852



728
704



729
788



730
797



731
860



732
813



733
880



734
888



735
933



736
561



737
689



738
698



739
775



740
719



741
791



742
800



743
867



744
731



745
810



746
825



747
884



748
838



749
894



750
907



751
949



752
766



753
819



754
846



755
897



756
858



757
911



758
916



759
961



760
868



761
921



762
929



763
966



764
940



765
974



766
983



767
1003



768
125



769
230



770
256



771
374



772
272



773
398



774
413



775
530



776
289



777
429



778
441



779
543



780
458



781
564



782
582



783
701



784
310



785
450



786
472



787
579



788
489



789
600



790
602



791
706



792
504



793
614



794
636



795
728



796
646



797
736



798
749



799
829



800
360



801
485



802
502



803
601



804
538



805
623



806
637



807
739



808
542



809
643



810
655



811
746



812
663



813
759



814
769



815
850



816
548



817
661



818
679



819
768



820
703



821
781



822
795



823
864



824
716



825
804



826
812



827
873



828
826



829
889



830
900



831
944



832
376



833
537



834
540



835
641



836
549



837
652



838
668



839
762



840
563



841
684



842
697



843
785



844
711



845
792



846
808



847
876



848
629



849
702



850
720



851
796



852
732



853
817



854
827



855
886



856
761



857
831



858
840



859
898



860
857



861
910



862
915



863
960



864
654



865
734



866
748



867
821



868
767



869
847



870
853



871
902



872
777



873
841



874
863



875
914



876
874



877
922



878
932



879
969



880
799



881
869



882
881



883
928



884
891



885
935



886
943



887
976



888
904



889
947



890
953



891
981



892
958



893
989



894
991



895
1011



896
385



897
551



898
562



899
699



900
622



901
708



902
717



903
802



904
642



905
727



906
737



907
823



908
757



909
830



910
849



911
901



912
657



913
752



914
765



915
835



916
776



917
851



918
862



919
913



920
793



921
872



922
859



923
919



924
887



925
931



926
939



927
972



928
705



929
771



930
779



931
855



932
805



933
866



934
878



935
926



936
815



937
882



938
892



939
936



940
899



941
941



942
950



943
980



944
839



945
895



946
906



947
945



948
917



949
955



950
959



951
987



952
923



953
965



954
968



955
993



956
975



957
996



958
998



959
1008



960
733



961
784



962
811



963
883



964
832



965
890



966
896



967
942



968
843



969
908



970
912



971
952



972
920



973
956



974
967



975
990



976
861



977
918



978
927



979
964



980
938



981
970



982
971



983
997



984
948



985
977



986
979



987
999



988
985



989
1004



990
1006



991
1016



992
877



993
934



994
937



995
973



996
951



997
978



998
982



999
1001



1000
957



1001
986



1002
988



1003
1005



1004
994



1005
1007



1006
1012



1007
1018



1008
962



1009
992



1010
995



1011
1009



1012
1000



1013
1010



1014
1013



1015
1019



1016
1002



1017
1014



1018
1015



1019
1020



1020
1017



1021
1021



1022
1022



1023
1023










Sequence Z7, having a sequence length of 512:

    • [0, 1, 2, 7, 3, 8, 11, 24, 4, 10, 13, 27, 16, 30, 34, 70, 5, 12, 14, 31, 21, 37, 45, 73, 20, 44, 41, 81, 54, 88, 93, 141, 6, 17, 23, 39, 19, 43, 47, 82, 28, 52, 56, 89, 65, 99, 103, 152, 33, 57, 67, 101, 71, 109, 116, 165, 77, 118, 126, 177, 131, 187, 199, 269, 9, 22, 26, 51, 29, 55, 62, 95, 35, 68, 58, 104, 75, 112, 121, 169, 42, 66, 76, 117, 84, 124, 130, 183, 91, 133, 145, 193, 151, 205, 215, 286, 49, 80, 90, 129, 100, 137, 149, 202, 107, 150, 164, 214, 171, 225, 234, 299, 119, 167, 182, 228, 185, 235, 247, 313, 196, 252, 259, 323, 273, 334, 347, 406, 15, 25, 32, 63, 38, 69, 74, 120, 46, 79, 85, 128, 92, 136, 140, 201, 53, 86, 94, 138, 102, 146, 155, 210, 111, 161, 168, 220, 179, 230, 245, 309, 60, 98, 108, 154, 113, 162, 173, 229, 127, 178, 186, 237, 195, 251, 262, 322, 139, 190, 203, 254, 213, 268, 275, 332, 226, 281, 293, 345, 302, 356, 372, 407, 64, 110, 123, 174, 135, 184, 194, 253, 143, 197, 206, 263, 216, 274, 285, 342, 156, 211, 221, 279, 236, 295, 301, 358, 242, 306, 315, 366, 327, 378, 387, 435, 170, 231, 239, 297, 255, 308, 317, 369, 272, 319, 333, 381, 346, 390, 398, 442, 284, 335, 348, 393, 355, 402, 412, 458, 370, 415, 422, 453, 429, 460, 469, 488, 18, 36, 40, 83, 48, 87, 96, 144, 50, 97, 105, 158, 114, 172, 175, 246, 59, 106, 115, 176, 125, 181, 189, 248, 132, 188, 200, 261, 212, 271, 276, 331, 61, 122, 134, 180, 142, 191, 204, 270, 153, 209, 217, 277, 224, 291, 298, 354, 159, 223, 232, 290, 241, 303, 311, 365, 257, 320, 324, 377, 336, 386, 395, 439, 72, 147, 148, 207, 160, 219, 227, 287, 166, 233, 238, 305, 249, 312, 321, 374, 198, 244, 256, 314, 264, 325, 337, 384, 283, 338, 350, 392, 359, 405, 409, 450, 218, 266, 278, 330, 289, 344, 352, 399, 300, 357, 364, 414, 375, 417, 426, 459, 316, 371, 379, 423, 385, 430, 419, 461, 396, 437, 444, 470, 448, 477, 482, 495, 78, 157, 163, 240, 192, 250, 258, 318, 208, 260, 267, 329, 282, 339, 349, 401, 222, 280, 288, 343, 294, 353, 361, 408, 307, 363, 367, 416, 383, 425, 433, 465, 243, 292, 296, 360, 310, 368, 376, 420, 328, 380, 388, 432, 397, 428, 441, 471, 341, 391, 403, 438, 410, 446, 452, 475, 418, 456, 455, 481, 462, 484, 487, 501, 265, 304, 326, 382, 340, 389, 394, 436, 351, 404, 400, 445, 413, 443, 454, 479, 362, 411, 421, 451, 427, 457, 463, 485, 434, 467, 468, 489, 474, 492, 494, 504, 373, 424, 431, 464, 440, 466, 473, 490, 447, 472, 476, 496, 480, 493, 499, 506, 449, 478, 483, 497, 486, 500, 498, 507, 491, 502, 503, 508, 505, 509, 510, 511]












Table Z7, having a sequence length of 512:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
11



7
24



8
4



9
10



10
13



11
27



12
16



13
30



14
34



15
70



16
5



17
12



18
14



19
31



20
21



21
37



22
45



23
73



24
20



25
44



26
41



27
81



28
54



29
88



30
93



31
141



32
6



33
17



34
23



35
39



36
19



37
43



38
47



39
82



40
28



41
52



42
56



43
89



44
65



45
99



46
103



47
152



48
33



49
57



50
67



51
101



52
71



53
109



54
116



55
165



56
77



57
118



58
126



59
177



60
131



61
187



62
199



63
269



64
9



65
22



66
26



67
51



68
29



69
55



70
62



71
95



72
35



73
68



74
58



75
104



76
75



77
112



78
121



79
169



80
42



81
66



82
76



83
117



84
84



85
124



86
130



87
183



88
91



89
133



90
145



91
193



92
151



93
205



94
215



95
286



96
49



97
80



98
90



99
129



100
100



101
137



102
149



103
202



104
107



105
150



106
164



107
214



108
171



109
225



110
234



111
299



112
119



113
167



114
182



115
228



116
185



117
235



118
247



119
313



120
196



121
252



122
259



123
323



124
273



125
334



126
347



127
406



128
15



129
25



130
32



131
63



132
38



133
69



134
74



135
120



136
46



137
79



138
85



139
128



140
92



141
136



142
140



143
201



144
53



145
86



146
94



147
138



148
102



149
146



150
155



151
210



152
111



153
161



154
168



155
220



156
179



157
230



158
245



159
309



160
60



161
98



162
108



163
154



164
113



165
162



166
173



167
229



168
127



169
178



170
186



171
237



172
195



173
251



174
262



175
322



176
139



177
190



178
203



179
254



180
213



181
268



182
275



183
332



184
226



185
281



186
293



187
345



188
302



189
356



190
372



191
407



192
64



193
110



194
123



195
174



196
135



197
184



198
194



199
253



200
143



201
197



202
206



203
263



204
216



205
274



206
285



207
342



208
156



209
211



210
221



211
279



212
236



213
295



214
301



215
358



216
242



217
306



218
315



219
366



220
327



221
378



222
387



223
435



224
170



225
231



226
239



227
297



228
255



229
308



230
317



231
369



232
272



233
319



234
333



235
381



236
346



237
390



238
398



239
442



240
284



241
335



242
348



243
393



244
355



245
402



246
412



247
458



248
370



249
415



250
422



251
453



252
429



253
460



254
469



255
488



256
18



257
36



258
40



259
83



260
48



261
87



262
96



263
144



264
50



265
97



266
105



267
158



268
114



269
172



270
175



271
246



272
59



273
106



274
115



275
176



276
125



277
181



278
189



279
248



280
132



281
188



282
200



283
261



284
212



285
271



286
276



287
331



288
61



289
122



290
134



291
180



292
142



293
191



294
204



295
270



296
153



297
209



298
217



299
277



300
224



301
291



302
298



303
354



304
159



305
223



306
232



307
290



308
241



309
303



310
311



311
365



312
257



313
320



314
324



315
377



316
336



317
386



318
395



319
439



320
72



321
147



322
148



323
207



324
160



325
219



326
227



327
287



328
166



329
233



330
238



331
305



332
249



333
312



334
321



335
374



336
198



337
244



338
256



339
314



340
264



341
325



342
337



343
384



344
283



345
338



346
350



347
392



348
359



349
405



350
409



351
450



352
218



353
266



354
278



355
330



356
289



357
344



358
352



359
399



360
300



361
357



362
364



363
414



364
375



365
417



366
426



367
459



368
316



369
371



370
379



371
423



372
385



373
430



374
419



375
461



376
396



377
437



378
444



379
470



380
448



381
477



382
482



383
495



384
78



385
157



386
163



387
240



388
192



389
250



390
258



391
318



392
208



393
260



394
267



395
329



396
282



397
339



398
349



399
401



400
222



401
280



402
288



403
343



404
294



405
353



406
361



407
408



408
307



409
363



410
367



411
416



412
383



413
425



414
433



415
465



416
243



417
292



418
296



419
360



420
310



421
368



422
376



423
420



424
328



425
380



426
388



427
432



428
397



429
428



430
441



431
471



432
341



433
391



434
403



435
438



436
410



437
446



438
452



439
475



440
418



441
456



442
455



443
481



444
462



445
484



446
487



447
501



448
265



449
304



450
326



451
382



452
340



453
389



454
394



455
436



456
351



457
404



458
400



459
445



460
413



461
443



462
454



463
479



464
362



465
411



466
421



467
451



468
427



469
457



470
463



471
485



472
434



473
467



474
468



475
489



476
474



477
492



478
494



479
504



480
373



481
424



482
431



483
464



484
440



485
466



486
473



487
490



488
447



489
472



490
476



491
496



492
480



493
493



494
499



495
506



496
449



497
478



498
483



499
497



500
486



501
500



502
498



503
507



504
491



505
502



506
503



507
508



508
505



509
509



510
510



511
511










Sequence Z8, having a sequence length of 256:

    • [0, 1, 2, 7, 3, 8, 11, 23, 4, 10, 13, 26, 16, 29, 33, 63, 5, 12, 14, 30, 20, 35, 42, 65, 19, 41, 38, 72, 49, 77, 82, 120, 6, 17, 22, 37, 18, 40, 44, 73, 27, 47, 51, 78, 58, 86, 90, 127, 32, 52, 60, 88, 64, 94, 99, 134, 69, 101, 107, 142, 112, 150, 157, 194, 9, 21, 25, 46, 28, 50, 55, 84, 34, 61, 53, 91, 67, 97, 104, 137, 39, 59, 68, 100, 74, 106, 111, 146, 80, 113, 122, 152, 126, 161, 167, 203, 45, 71, 79, 110, 87, 116, 124, 159, 92, 125, 133, 166, 139, 171, 177, 207, 102, 135, 145, 173, 148, 178, 184, 213, 155, 186, 190, 218, 196, 222, 227, 243, 15, 24, 31, 56, 36, 62, 66, 103, 43, 70, 75, 109, 81, 115, 119, 158, 48, 76, 83, 117, 89, 123, 129, 163, 96, 131, 136, 169, 144, 175, 183, 212, 54, 85, 93, 128, 98, 132, 140, 174, 108, 143, 149, 180, 154, 185, 191, 217, 118, 151, 160, 188, 165, 193, 198, 220, 172, 200, 204, 225, 209, 230, 235, 244, 57, 95, 105, 141, 114, 147, 153, 187, 121, 156, 162, 192, 168, 197, 202, 224, 130, 164, 170, 199, 179, 205, 208, 231, 182, 210, 214, 232, 219, 236, 238, 249, 138, 176, 181, 206, 189, 211, 215, 233, 195, 216, 221, 237, 226, 239, 241, 250, 201, 223, 228, 240, 229, 242, 245, 252, 234, 246, 247, 251, 248, 253, 254, 255]









TABLE Z8







having a sequence length of 256:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
11



7
23



8
4



9
10



10
13



11
26



12
16



13
29



14
33



15
63



16
5



17
12



18
14



19
30



20
20



21
35



22
42



23
65



24
19



25
41



26
38



27
72



28
49



29
77



30
82



31
120



32
6



33
17



34
22



35
37



36
18



37
40



38
44



39
73



40
27



41
47



42
51



43
78



44
58



45
86



46
90



47
127



48
32



49
52



50
60



51
88



52
64



53
94



54
99



55
134



56
69



57
101



58
107



59
142



60
112



61
150



62
157



63
194



64
9



65
21



66
25



67
46



68
28



69
50



70
55



71
84



72
34



73
61



74
53



75
91



76
67



77
97



78
104



79
137



80
39



81
59



82
68



83
100



84
74



85
106



86
111



87
146



88
80



89
113



90
122



91
152



92
126



93
161



94
167



95
203



96
45



97
71



98
79



99
110



100
87



101
116



102
124



103
159



104
92



105
125



106
133



107
166



108
139



109
171



110
177



111
207



112
102



113
135



114
145



115
173



116
148



117
178



118
184



119
213



120
155



121
186



122
190



123
218



124
196



125
222



126
227



127
243



128
15



129
24



130
31



131
56



132
36



133
62



134
66



135
103



136
43



137
70



138
75



139
109



140
81



141
115



142
119



143
158



144
48



145
76



146
83



147
117



148
89



149
123



150
129



151
163



152
96



153
131



154
136



155
169



156
144



157
175



158
183



159
212



160
54



161
85



162
93



163
128



164
98



165
132



166
140



167
174



168
108



169
143



170
149



171
180



172
154



173
185



174
191



175
217



176
118



177
151



178
160



179
188



180
165



181
193



182
198



183
220



184
172



185
200



186
204



187
225



188
209



189
230



190
235



191
244



192
57



193
95



194
105



195
141



196
114



197
147



198
153



199
187



200
121



201
156



202
162



203
192



204
168



205
197



206
202



207
224



208
130



209
164



210
170



211
199



212
179



213
205



214
208



215
231



216
182



217
210



218
214



219
232



220
219



221
236



222
238



223
249



224
138



225
176



226
181



227
206



228
189



229
211



230
215



231
233



232
195



233
216



234
221



235
237



236
226



237
239



238
241



239
250



240
201



241
223



242
228



243
240



244
229



245
242



246
245



247
252



248
234



249
246



250
247



251
251



252
248



253
253



254
254



255
255










Sequence Z9, having a sequence length of 128:

    • [0, 1, 2, 7, 3, 8, 11, 22, 4, 10, 13, 24, 15, 27, 30, 53, 5, 12, 14, 28, 19, 32, 38, 55, 18, 37, 34, 60, 43, 63, 67, 89, 6, 16, 21, 33, 17, 36, 39, 61, 25, 42, 45, 64, 49, 69, 72, 94, 29, 46, 51, 71, 54, 75, 77, 96, 58, 79, 83, 100, 86, 104, 107, 119, 9, 20, 23, 41, 26, 44, 48, 68, 31, 52, 47, 73, 56, 76, 81, 98, 35, 50, 57, 78, 62, 82, 85, 102, 66, 87, 90, 105, 93, 109, 111, 121, 40, 59, 65, 84, 70, 88, 91, 108, 74, 92, 95, 110, 99, 112, 114, 122, 80, 97, 101, 113, 103, 115, 116, 123, 106, 117, 118, 124, 120, 125, 126, 127]












TABLE Z9, having a sequence length of 128:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
11



7
22



8
4



9
10



10
13



11
24



12
15



13
27



14
30



15
53



16
5



17
12



18
14



19
28



20
19



21
32



22
38



23
55



24
18



25
37



26
34



27
60



28
43



29
63



30
67



31
89



32
6



33
16



34
21



35
33



36
17



37
36



38
39



39
61



40
25



41
42



42
45



43
64



44
49



45
69



46
72



47
94



48
29



49
46



50
51



51
71



52
54



53
75



54
77



55
96



56
58



57
79



58
83



59
100



60
86



61
104



62
107



63
119



64
9



65
20



66
23



67
41



68
26



69
44



70
48



71
68



72
31



73
52



74
47



75
73



76
56



77
76



78
81



79
98



80
35



81
50



82
57



83
78



84
62



85
82



86
85



87
102



88
66



89
87



90
90



91
105



92
93



93
109



94
111



95
121



96
40



97
59



98
65



99
84



100
70



101
88



102
91



103
108



104
74



105
92



106
95



107
110



108
99



109
112



110
114



111
122



112
80



113
97



114
101



115
113



116
103



117
115



118
116



119
123



120
106



121
117



122
118



123
124



124
120



125
125



126
126



127
127










Sequence Z10, having a sequence length of 64:

    • [0, 1, 2, 7, 3, 8, 10, 20, 4, 9, 12, 21, 14, 23, 26, 40, 5, 11, 13, 24, 18, 27, 32, 42, 17, 31, 29, 44, 35, 46, 48, 57, 6, 15, 19, 28, 16, 30, 33, 45, 22, 34, 36, 47, 38, 49, 51, 58, 25, 37, 39, 50, 41, 52, 53, 59, 43, 54, 55, 60, 56, 61, 62, 63]












Table Z10, having a sequence length of 64:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
2



3
7



4
3



5
8



6
10



7
20



8
4



9
9



10
12



11
21



12
14



13
23



14
26



15
40



16
5



17
11



18
13



19
24



20
18



21
27



22
32



23
42



24
17



25
31



26
29



27
44



28
35



29
46



30
48



31
57



32
6



33
15



34
19



35
28



36
16



37
30



38
33



39
45



40
22



41
34



42
36



43
47



44
38



45
49



46
51



47
58



48
25



49
37



50
39



51
50



52
41



53
52



54
53



55
59



56
43



57
54



58
55



59
60



60
56



61
61



62
62



63
63










Third group of sequences (a criterion that comprehensively considers performance obtained by List (list) whose sizes are respectively 1, 2, 4, 8, and 16, and preferentially considers performance of Lists 2, 4, and 8).


Sequence Q11, having a sequence length of 1024:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 65, 20, 256, 34, 24, 36, 7, 129, 66, 512, 11, 40, 68, 130, 19, 13, 48, 14, 72, 257, 21, 132, 35, 258, 26, 513, 80, 37, 25, 22, 136, 260, 264, 38, 514, 96, 67, 41, 144, 28, 69, 42, 516, 49, 74, 272, 160, 520, 288, 528, 192, 544, 70, 44, 131, 81, 50, 73, 15, 320, 133, 52, 23, 134, 384, 76, 137, 82, 56, 27, 97, 39, 259, 84, 138, 145, 261, 29, 43, 98, 515, 88, 140, 30, 146, 71, 262, 265, 161, 576, 45, 100, 640, 51, 148, 46, 75, 266, 273, 517, 104, 162, 53, 193, 152, 77, 164, 768, 268, 274, 518, 54, 83, 57, 521, 112, 135, 78, 289, 194, 85, 276, 522, 58, 168, 139, 99, 86, 60, 280, 89, 290, 529, 524, 196, 141, 101, 147, 176, 142, 530, 321, 31, 200, 90, 545, 292, 322, 532, 263, 149, 102, 105, 304, 296, 163, 92, 47, 267, 385, 546, 324, 208, 386, 150, 153, 165, 106, 55, 328, 536, 577, 548, 113, 154, 79, 269, 108, 578, 224, 166, 519, 552, 195, 270, 641, 523, 275, 580, 291, 59, 169, 560, 114, 277, 156, 87, 197, 116, 170, 61, 531, 525, 642, 281, 278, 526, 177, 293, 388, 91, 584, 769, 198, 172, 120, 201, 336, 62, 282, 143, 103, 178, 294, 93, 644, 202, 592, 323, 392, 297, 770, 107, 180, 151, 209, 284, 648, 94, 204, 298, 400, 608, 352, 325, 533, 155, 210, 305, 547, 300, 109, 184, 534, 537, 115, 167, 225, 326, 306, 772, 157, 656, 329, 110, 117, 212, 171, 776, 330, 226, 549, 538, 387, 308, 216, 416, 271, 279, 158, 337, 550, 672, 118, 332, 579, 540, 389, 173, 121, 553, 199, 784, 179, 228, 338, 312, 704, 390, 174, 554, 581, 393, 283, 122, 448, 353, 561, 203, 63, 340, 394, 527, 582, 556, 181, 295, 285, 232, 124, 205, 182, 643, 562, 286, 585, 299, 354, 211, 401, 185, 396, 344, 586, 645, 593, 535, 240, 206, 95, 327, 564, 800, 402, 356, 307, 301, 417, 213, 568, 832, 588, 186, 646, 404, 227, 896, 594, 418, 302, 649, 771, 360, 539, 111, 331, 214, 309, 188, 449, 217, 408, 609, 596, 551, 650, 229, 159, 420, 310, 541, 773, 610, 657, 333, 119, 600, 339, 218, 368, 652, 230, 391, 313, 450, 542, 334, 233, 555, 774, 175, 123, 658, 612, 341, 777, 220, 314, 424, 395, 673, 583, 355, 287, 183, 234, 125, 557, 660, 616, 342, 316, 241, 778, 563, 345, 452, 397, 403, 207, 674, 558, 785, 432, 357, 187, 236, 664, 624, 587, 780, 705, 126, 242, 565, 398, 346, 456, 358, 405, 303, 569, 244, 595, 189, 566, 676, 361, 706, 589, 215, 786, 647, 348, 419, 406, 464, 680, 801, 362, 590, 409, 570, 788, 597, 572, 219, 311, 708, 598, 601, 651, 421, 792, 802, 611, 602, 410, 231, 688, 653, 248, 369, 190, 364, 654, 659, 335, 480, 315, 221, 370, 613, 422, 425, 451, 614, 543, 235, 412, 343, 372, 775, 317, 222, 426, 453, 237, 559, 833, 804, 712, 834, 661, 808, 779, 617, 604, 433, 720, 816, 836, 347, 897, 243, 662, 454, 318, 675, 618, 898, 781, 376, 428, 665, 736, 567, 840, 625, 238, 359, 457, 399, 787, 591, 678, 434, 677, 349, 245, 458, 666, 620, 363, 127, 191, 782, 407, 436, 626, 571, 465, 681, 246, 707, 350, 599, 668, 790, 460, 249, 682, 573, 411, 803, 789, 709, 365, 440, 628, 689, 374, 423, 466, 793, 250, 371, 481, 574, 413, 603, 366, 468, 655, 900, 805, 615, 684, 710, 429, 794, 252, 373, 605, 848, 690, 713, 632, 482, 806, 427, 904, 414, 223, 663, 692, 835, 619, 472, 455, 796, 809, 714, 721, 837, 716, 864, 810, 606, 912, 722, 696, 377, 435, 817, 319, 621, 812, 484, 430, 838, 667, 488, 239, 378, 459, 622, 627, 437, 380, 818, 461, 496, 669, 679, 724, 841, 629, 351, 467, 438, 737, 251, 462, 442, 441, 469, 247, 683, 842, 738, 899, 670, 783, 849, 820, 728, 928, 791, 367, 901, 630, 685, 844, 633, 711, 253, 691, 824, 902, 686, 740, 850, 375, 444, 470, 483, 415, 485, 905, 795, 473, 634, 744, 852, 960, 865, 693, 797, 906, 715, 807, 474, 636, 694, 254, 717, 575, 913, 798, 811, 379, 697, 431, 607, 489, 866, 723, 486, 908, 718, 813, 476, 856, 839, 725, 698, 914, 752, 868, 819, 814, 439, 929, 490, 623, 671, 739, 916, 463, 843, 381, 497, 930, 821, 726, 961, 872, 492, 631, 729, 700, 443, 741, 845, 920, 382, 822, 851, 730, 498, 880, 742, 445, 471, 635, 932, 687, 903, 825, 500, 846, 745, 826, 732, 446, 962, 936, 475, 853, 867, 637, 907, 487, 695, 746, 828, 753, 854, 857, 504, 799, 255, 964, 909, 719, 477, 915, 638, 748, 944, 869, 491, 699, 754, 858, 478, 968, 383, 910, 815, 976, 870, 917, 727, 493, 873, 701, 931, 756, 860, 499, 731, 823, 922, 874, 918, 502, 933, 743, 760, 881, 494, 702, 921, 501, 876, 847, 992, 447, 733, 827, 934, 882, 937, 963, 747, 505, 855, 924, 734, 829, 965, 938, 884, 506, 749, 945, 966, 755, 859, 940, 830, 911, 871, 639, 888, 479, 946, 750, 969, 508, 861, 757, 970, 919, 875, 862, 758, 948, 977, 923, 972, 761, 877, 952, 495, 703, 935, 978, 883, 762, 503, 925, 878, 735, 993, 885, 939, 994, 980, 926, 764, 941, 967, 886, 831, 947, 507, 889, 984, 751, 942, 996, 971, 890, 509, 949, 973, 1000, 892, 950, 863, 759, 1008, 510, 979, 953, 763, 974, 954, 879, 981, 982, 927, 995, 765, 956, 887, 985, 997, 986, 943, 891, 998, 766, 511, 988, 1001, 951, 1002, 893, 975, 894, 1009, 955, 1004, 1010, 957, 983, 958, 987, 1012, 999, 1016, 767, 989, 1003, 990, 1005, 959, 1011, 1013, 895, 1006, 1014, 1017, 1018, 991, 1020, 1007, 1015, 1019, 1021, 1022, 1023]









TABLE Q11







having a sequence length of 1024:










Reliability
Polarized



or sequence
channel



number of
sequence



reliability
number














0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
64



10
9



11
6



12
17



13
10



14
18



15
128



16
12



17
33



18
65



19
20



20
256



21
34



22
24



23
36



24
7



25
129



26
66



27
512



28
11



29
40



30
68



31
130



32
19



33
13



34
48



35
14



36
72



37
257



38
21



39
132



40
35



41
258



42
26



43
513



44
80



45
37



46
25



47
22



48
136



49
260



50
264



51
38



52
514



53
96



54
67



55
41



56
144



57
28



58
69



59
42



60
516



61
49



62
74



63
272



64
160



65
520



66
288



67
528



68
192



69
544



70
70



71
44



72
131



73
81



74
50



75
73



76
15



77
320



78
133



79
52



80
23



81
134



82
384



83
76



84
137



85
82



86
56



87
27



88
97



89
39



90
259



91
84



92
138



93
145



94
261



95
29



96
43



97
98



98
515



99
88



100
140



101
30



102
146



103
71



104
262



105
265



106
161



107
576



108
45



109
100



110
640



111
51



112
148



113
46



114
75



115
266



116
273



117
517



118
104



119
162



120
53



121
193



122
152



123
77



124
164



125
768



126
268



127
274



128
518



129
54



130
83



131
57



132
521



133
112



134
135



135
78



136
289



137
194



138
85



139
276



140
522



141
58



142
168



143
139



144
99



145
86



146
60



147
280



148
89



149
290



150
529



151
524



152
196



153
141



154
101



155
147



156
176



157
142



158
530



159
321



160
31



161
200



162
90



163
545



164
292



165
322



166
532



167
263



168
149



169
102



170
105



171
304



172
296



173
163



174
92



175
47



176
267



177
385



178
546



179
324



180
208



181
386



182
150



183
153



184
165



185
106



186
55



187
328



188
536



189
577



190
548



191
113



192
154



193
79



194
269



195
108



196
578



197
224



198
166



199
519



200
552



201
195



202
270



203
641



204
523



205
275



206
580



207
291



208
59



209
169



210
560



211
114



212
277



213
156



214
87



215
197



216
116



217
170



218
61



219
531



220
525



221
642



222
281



223
278



224
526



225
177



226
293



227
388



228
91



229
584



230
769



231
198



232
172



233
120



234
201



235
336



236
62



237
282



238
143



239
103



240
178



241
294



242
93



243
644



244
202



245
592



246
323



247
392



248
297



249
770



250
107



251
180



252
151



253
209



254
284



255
648



256
94



257
204



258
298



259
400



260
608



261
352



262
325



263
533



264
155



265
210



266
305



267
547



268
300



269
109



270
184



271
534



272
537



273
115



274
167



275
225



276
326



277
306



278
772



279
157



280
656



281
329



282
110



283
117



284
212



285
171



286
776



287
330



288
226



289
549



290
538



291
387



292
308



293
216



294
416



295
271



296
279



297
158



298
337



299
550



300
672



301
118



302
332



303
579



304
540



305
389



306
173



307
121



308
553



309
199



310
784



311
179



312
228



313
338



314
312



315
704



316
390



317
174



318
554



319
581



320
393



321
283



322
122



323
448



324
353



325
561



326
203



327
63



328
340



329
394



330
527



331
582



332
556



333
181



334
295



335
285



336
232



337
124



338
205



339
182



340
643



341
562



342
286



343
585



344
299



345
354



346
211



347
401



348
185



349
396



350
344



351
586



352
645



353
593



354
535



355
240



356
206



357
95



358
327



359
564



360
800



361
402



362
356



363
307



364
301



365
417



366
213



367
568



368
832



369
588



370
186



371
646



372
404



373
227



374
896



375
594



376
418



377
302



378
649



379
771



380
360



381
539



382
111



383
331



384
214



385
309



386
188



387
449



388
217



389
408



390
609



391
596



392
551



393
650



394
229



395
159



396
420



397
310



398
541



399
773



400
610



401
657



402
333



403
119



404
600



405
339



406
218



407
368



408
652



409
230



410
391



411
313



412
450



413
542



414
334



415
233



416
555



417
774



418
175



419
123



420
658



421
612



422
341



423
777



424
220



425
314



426
424



427
395



428
673



429
583



430
355



431
287



432
183



433
234



434
125



435
557



436
660



437
616



438
342



439
316



440
241



441
778



442
563



443
345



444
452



445
397



446
403



447
207



448
674



449
558



450
785



451
432



452
357



453
187



454
236



455
664



456
624



457
587



458
780



459
705



460
126



461
242



462
565



463
398



464
346



465
456



466
358



467
405



468
303



469
569



470
244



471
595



472
189



473
566



474
676



475
361



476
706



477
589



478
215



479
786



480
647



481
348



482
419



483
406



484
464



485
680



486
801



487
362



488
590



489
409



490
570



491
788



492
597



493
572



494
219



495
311



496
708



497
598



498
601



499
651



500
421



501
792



502
802



503
611



504
602



505
410



506
231



507
688



508
653



509
248



510
369



511
190



512
364



513
654



514
659



515
335



516
480



517
315



518
221



519
370



520
613



521
422



522
425



523
451



524
614



525
543



526
235



527
412



528
343



529
372



530
775



531
317



532
222



533
426



534
453



535
237



536
559



537
833



538
804



539
712



540
834



541
661



542
808



543
779



544
617



545
604



546
433



547
720



548
816



549
836



550
347



551
897



552
243



553
662



554
454



555
318



556
675



557
618



558
898



559
781



560
376



561
428



562
665



563
736



564
567



565
840



566
625



567
238



568
359



569
457



570
399



571
787



572
591



573
678



574
434



575
677



576
349



577
245



578
458



579
666



580
620



581
363



582
127



583
191



584
782



585
407



586
436



587
626



588
571



589
465



590
681



591
246



592
707



593
350



594
599



595
668



596
790



597
460



598
249



599
682



600
573



601
411



602
803



603
789



604
709



605
365



606
440



607
628



608
689



609
374



610
423



611
466



612
793



613
250



614
371



615
481



616
574



617
413



618
603



619
366



620
468



621
655



622
900



623
805



624
615



625
684



626
710



627
429



628
794



629
252



630
373



631
605



632
848



633
690



634
713



635
632



636
482



637
806



638
427



639
904



640
414



641
223



642
663



643
692



644
835



645
619



646
472



647
455



648
796



649
809



650
714



651
721



652
837



653
716



654
864



655
810



656
606



657
912



658
722



659
696



660
377



661
435



662
817



663
319



664
621



665
812



666
484



667
430



668
838



669
667



670
488



671
239



672
378



673
459



674
622



675
627



676
437



677
380



678
818



679
461



680
496



681
669



682
679



683
724



684
841



685
629



686
351



687
467



688
438



689
737



690
251



691
462



692
442



693
441



694
469



695
247



696
683



697
842



698
738



699
899



700
670



701
783



702
849



703
820



704
728



705
928



706
791



707
367



708
901



709
630



710
685



711
844



712
633



713
711



714
253



715
691



716
824



717
902



718
686



719
740



720
850



721
375



722
444



723
470



724
483



725
415



726
485



727
905



728
795



729
473



730
634



731
744



732
852



733
960



734
865



735
693



736
797



737
906



738
715



739
807



740
474



741
636



742
694



743
254



744
717



745
575



746
913



747
798



748
811



749
379



750
697



751
431



752
607



753
489



754
866



755
723



756
486



757
908



758
718



759
813



760
476



761
856



762
839



763
725



764
698



765
914



766
752



767
868



768
819



769
814



770
439



771
929



772
490



773
623



774
671



775
739



776
916



777
463



778
843



779
381



780
497



781
930



782
821



783
726



784
961



785
872



786
492



787
631



788
729



789
700



790
443



791
741



792
845



793
920



794
382



795
822



796
851



797
730



798
498



799
880



800
742



801
445



802
471



803
635



804
932



805
687



806
903



807
825



808
500



809
846



810
745



811
826



812
732



813
446



814
962



815
936



816
475



817
853



818
867



819
637



820
907



821
487



822
695



823
746



824
828



825
753



826
854



827
857



828
504



829
799



830
255



831
964



832
909



833
719



834
477



835
915



836
638



837
748



838
944



839
869



840
491



841
699



842
754



843
858



844
478



845
968



846
383



847
910



848
815



849
976



850
870



851
917



852
727



853
493



854
873



855
701



856
931



857
756



858
860



859
499



860
731



861
823



862
922



863
874



864
918



865
502



866
933



867
743



868
760



869
881



870
494



871
702



872
921



873
501



874
876



875
847



876
992



877
447



878
733



879
827



880
934



881
882



882
937



883
963



884
747



885
505



886
855



887
924



888
734



889
829



890
965



891
938



892
884



893
506



894
749



895
945



896
966



897
755



898
859



899
940



900
830



901
911



902
871



903
639



904
888



905
479



906
946



907
750



908
969



909
508



910
861



911
757



912
970



913
919



914
875



915
862



916
758



917
948



918
977



919
923



920
972



921
761



922
877



923
952



924
495



925
703



926
935



927
978



928
883



929
762



930
503



931
925



932
878



933
735



934
993



935
885



936
939



937
994



938
980



939
926



940
764



941
941



942
967



943
886



944
831



945
947



946
507



947
889



948
984



949
751



950
942



951
996



952
971



953
890



954
509



955
949



956
973



957
1000



958
892



959
950



960
863



961
759



962
1008



963
510



964
979



965
953



966
763



967
974



968
954



969
879



970
981



971
982



972
927



973
995



974
765



975
956



976
887



977
985



978
997



979
986



980
943



981
891



982
998



983
766



984
511



985
988



986
1001



987
951



988
1002



989
893



990
975



991
894



992
1009



993
955



994
1004



995
1010



996
957



997
983



998
958



999
987



1000
1012



1001
999



1002
1016



1003
767



1004
989



1005
1003



1006
990



1007
1005



1008
959



1009
1011



1010
1013



1011
895



1012
1006



1013
1014



1014
1017



1015
1018



1016
991



1017
1020



1018
1007



1019
1015



1020
1019



1021
1021



1022
1022



1023
1023










Sequence Q12, having a sequence length of 512:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 65, 20, 256, 34, 24, 36, 7, 129, 66, 11, 40, 68, 130, 19, 13, 48, 14, 72, 257, 21, 132, 35, 258, 26, 80, 37, 25, 22, 136, 260, 264, 38, 96, 67, 41, 144, 28, 69, 42, 49, 74, 272, 160, 288, 192, 70, 44, 131, 81, 50, 73, 15, 320, 133, 52, 23, 134, 384, 76, 137, 82, 56, 27, 97, 39, 259, 84, 138, 145, 261, 29, 43, 98, 88, 140, 30, 146, 71, 262, 265, 161, 45, 100, 51, 148, 46, 75, 266, 273, 104, 162, 53, 193, 152, 77, 164, 268, 274, 54, 83, 57, 112, 135, 78, 289, 194, 85, 276, 58, 168, 139, 99, 86, 60, 280, 89, 290, 196, 141, 101, 147, 176, 142, 321, 31, 200, 90, 292, 322, 263, 149, 102, 105, 304, 296, 163, 92, 47, 267, 385, 324, 208, 386, 150, 153, 165, 106, 55, 328, 113, 154, 79, 269, 108, 224, 166, 195, 270, 275, 291, 59, 169, 114, 277, 156, 87, 197, 116, 170, 61, 281, 278, 177, 293, 388, 91, 198, 172, 120, 201, 336, 62, 282, 143, 103, 178, 294, 93, 202, 323, 392, 297, 107, 180, 151, 209, 284, 94, 204, 298, 400, 352, 325, 155, 210, 305, 300, 109, 184, 115, 167, 225, 326, 306, 157, 329, 110, 117, 212, 171, 330, 226, 387, 308, 216, 416, 271, 279, 158, 337, 118, 332, 389, 173, 121, 199, 179, 228, 338, 312, 390, 174, 393, 283, 122, 448, 353, 203, 63, 340, 394, 181, 295, 285, 232, 124, 205, 182, 286, 299, 354, 211, 401, 185, 396, 344, 240, 206, 95, 327, 402, 356, 307, 301, 417, 213, 186, 404, 227, 418, 302, 360, 111, 331, 214, 309, 188, 449, 217, 408, 229, 159, 420, 310, 333, 119, 339, 218, 368, 230, 391, 313, 450, 334, 233, 175, 123, 341, 220, 314, 424, 395, 355, 287, 183, 234, 125, 342, 316, 241, 345, 452, 397, 403, 207, 432, 357, 187, 236, 126, 242, 398, 346, 456, 358, 405, 303, 244, 189, 361, 215, 348, 419, 406, 464, 362, 409, 219, 311, 421, 410, 231, 248, 369, 190, 364, 335, 480, 315, 221, 370, 422, 425, 451, 235, 412, 343, 372, 317, 222, 426, 453, 237, 433, 347, 243, 454, 318, 376, 428, 238, 359, 457, 399, 434, 349, 245, 458, 363, 127, 191, 407, 436, 465, 246, 350, 460, 249, 411, 365, 440, 374, 423, 466, 250, 371, 481, 413, 366, 468, 429, 252, 373, 482, 427, 414, 223, 472, 455, 377, 435, 319, 484, 430, 488, 239, 378, 459, 437, 380, 461, 496, 351, 467, 438, 251, 462, 442, 441, 469, 247, 367, 253, 375, 444, 470, 483, 415, 485, 473, 474, 254, 379, 431, 489, 486, 476, 439, 490, 463, 381, 497, 492, 443, 382, 498, 445, 471, 500, 446, 475, 487, 504, 255, 477, 491, 478, 383, 493, 499, 502, 494, 501, 447, 505, 506, 479, 508, 495, 503, 507, 509, 510, 511]









TABLE Q12







having a sequence length of 512:






















Reliability
Polarized
Reliability
Polarized
Reliability
Polarized
Reliability
Polarized
Reliability
Polarized
Reliability
Polarized
Reliability
Polarized
Reliability
Polarized


or sequence
channel
or sequence
channel
or sequence
channel
or sequence
channel
or sequence
channel
or sequence
channel
or sequence
channel
or sequence
channel


number of
sequence
number of
sequence
number of
sequence
number of
sequence
number of
sequence
number of
sequence
number of
sequence
number of
sequence


reliability
number
reliability
number
reliability
number
reliability
number
reliability
number
reliability
number
reliability
number
reliability
number

























0
0
64
44
128
139
192
388
256
338
320
450
384
343
448
461


1
1
65
131
129
99
193
91
257
312
321
334
385
372
449
496


2
2
66
81
130
86
194
198
258
390
322
233
386
317
450
351


3
4
67
50
131
60
195
172
259
174
323
175
387
222
451
467


4
8
68
73
132
280
196
120
260
393
324
123
388
426
452
438


5
16
69
15
133
89
197
201
261
283
325
341
389
453
453
251


6
32
70
320
134
290
198
336
262
122
326
220
390
237
454
462


7
3
71
133
135
196
199
62
263
448
327
314
391
433
455
442


8
5
72
52
136
141
200
282
264
353
328
424
392
347
456
441


9
64
73
23
137
101
201
143
265
203
329
395
393
243
457
469


10
9
74
134
138
147
202
103
266
63
330
355
394
454
458
247


11
6
75
384
139
176
203
178
267
340
331
287
395
318
459
367


12
17
76
76
140
142
204
294
268
394
332
183
396
376
460
253


13
10
77
137
141
321
205
93
269
181
333
234
397
428
461
375


14
18
78
82
142
31
206
202
270
295
334
125
398
238
462
444


15
128
79
56
143
200
207
323
271
285
335
342
399
359
463
470


16
12
80
27
144
90
208
392
272
232
336
316
400
457
464
483


17
33
81
97
145
292
209
297
273
124
337
241
401
399
465
415


18
65
82
39
146
322
210
107
274
205
338
345
402
434
466
485


19
20
83
259
147
263
211
180
275
182
339
452
403
349
467
473


20
256
84
84
148
149
212
151
276
286
340
397
404
245
468
474


21
34
85
138
149
102
213
209
277
299
341
403
405
458
469
254


22
24
86
145
150
105
214
284
278
354
342
207
406
363
470
379


23
36
87
261
151
304
215
94
279
211
343
432
407
127
471
431


24
7
88
29
152
296
216
204
280
401
344
357
408
191
472
489


25
129
89
43
153
163
217
298
281
185
345
187
409
407
473
486


26
66
90
98
154
92
218
400
282
396
346
236
410
436
474
476


27
11
91
88
155
47
219
352
283
344
347
126
411
465
475
439


28
40
92
140
156
267
220
325
284
240
348
242
412
246
476
490


29
68
93
30
157
385
221
155
285
206
349
398
413
350
477
463


30
130
94
146
158
324
222
210
286
95
350
346
414
460
478
381


31
19
95
71
159
208
223
305
287
327
351
456
415
249
479
497


32
13
96
262
160
386
224
300
288
402
352
358
416
411
480
492


33
48
97
265
161
150
225
109
289
356
353
405
417
365
481
443


34
14
98
161
162
153
226
184
290
307
354
303
418
440
482
382


35
72
99
45
163
165
227
115
291
301
355
244
419
374
483
498


36
257
100
100
164
106
228
167
292
417
356
189
420
423
484
445


37
21
101
51
165
55
229
225
293
213
357
361
421
466
485
471


38
132
102
148
166
328
230
326
294
186
358
215
422
250
486
500


39
35
103
46
167
113
231
306
295
404
359
348
423
371
487
446


43
37
107
104
171
108
235
117
299
360
363
362
427
468
491
255


44
25
108
162
172
224
236
212
300
111
364
409
428
429
492
477


45
22
109
53
173
166
237
171
301
331
365
219
429
252
493
491


46
136
110
193
174
195
238
330
302
214
366
311
430
373
494
478


47
260
111
152
175
270
239
226
303
309
367
421
431
482
495
383


48
264
112
77
176
275
240
387
304
188
368
410
432
427
496
493


49
38
113
164
177
291
241
308
305
449
369
231
433
414
497
499


50
96
114
268
178
59
242
216
306
217
370
248
434
223
498
502


51
67
115
274
179
169
243
416
307
408
371
369
435
472
499
494


52
41
116
54
180
114
244
271
308
229
372
190
436
455
500
501


53
144
117
83
181
277
245
279
309
159
373
364
437
377
501
447


54
28
118
57
182
156
246
158
310
420
374
335
438
435
502
505


55
69
119
112
183
87
247
337
311
310
375
480
439
319
503
506


56
42
120
135
184
197
248
118
312
333
376
315
440
484
504
479


57
49
121
78
185
116
249
332
313
119
377
221
441
430
505
508


58
74
122
289
186
170
250
389
314
339
378
370
442
488
506
495


59
272
123
194
187
61
251
173
315
218
379
422
443
239
507
503


60
160
124
85
188
281
252
121
316
368
380
425
444
378
508
507


61
288
125
276
189
278
253
199
317
230
381
451
445
459
509
509


62
192
126
58
190
177
254
179
318
391
382
235
446
437
510
510


63
70
127
168
191
293
255
228
319
313
383
412
447
380
511
511









Sequence Q13, having a sequence length of 256:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 65, 20, 34, 24, 36, 7, 129, 66, 11, 40, 68, 130, 19, 13, 48, 14, 72, 21, 132, 35, 26, 80, 37, 25, 22, 136, 38, 96, 67, 41, 144, 28, 69, 42, 49, 74, 160, 192, 70, 44, 131, 81, 50, 73, 15, 133, 52, 23, 134, 76, 137, 82, 56, 27, 97, 39, 84, 138, 145, 29, 43, 98, 88, 140, 30, 146, 71, 161, 45, 100, 51, 148, 46, 75, 104, 162, 53, 193, 152, 77, 164, 54, 83, 57, 112, 135, 78, 194, 85, 58, 168, 139, 99, 86, 60, 89, 196, 141, 101, 147, 176, 142, 31, 200, 90, 149, 102, 105, 163, 92, 47, 208, 150, 153, 165, 106, 55, 113, 154, 79, 108, 224, 166, 195, 59, 169, 114, 156, 87, 197, 116, 170, 61, 177, 91, 198, 172, 120, 201, 62, 143, 103, 178, 93, 202, 107, 180, 151, 209, 94, 204, 155, 210, 109, 184, 115, 167, 225, 157, 110, 117, 212, 171, 226, 216, 158, 118, 173, 121, 199, 179, 228, 174, 122, 203, 63, 181, 232, 124, 205, 182, 211, 185, 240, 206, 95, 213, 186, 227, 111, 214, 188, 217, 229, 159, 119, 218, 230, 233, 175, 123, 220, 183, 234, 125, 241, 207, 187, 236, 126, 242, 244, 189, 215, 219, 231, 248, 190, 221, 235, 222, 237, 243, 238, 245, 127, 191, 246, 249, 250, 252, 223, 239, 251, 247, 253, 254, 255]









TABLE Q13







having a sequence length of 256:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
64



10
9



11
6



12
17



13
10



14
18



15
128



16
12



17
33



18
65



19
20



20
34



21
24



22
36



23
7



24
129



25
66



26
11



27
40



28
68



29
130



30
19



31
13



32
48



33
14



34
72



35
21



36
132



37
35



38
26



39
80



40
37



41
25



42
22



43
136



44
38



45
96



46
67



47
41



48
144



49
28



50
69



51
42



52
49



53
74



54
160



55
192



56
70



57
44



58
131



59
81



60
50



61
73



62
15



63
133



64
52



65
23



66
134



67
76



68
137



69
82



70
56



71
27



72
97



73
39



74
84



75
138



76
145



77
29



78
43



79
98



80
88



81
140



82
30



83
146



84
71



85
161



86
45



87
100



88
51



89
148



90
46



91
75



92
104



93
162



94
53



95
193



96
152



97
77



98
164



99
54



100
83



101
57



102
112



103
135



104
78



105
194



106
85



107
58



108
168



109
139



110
99



111
86



112
60



113
89



114
196



115
141



116
101



117
147



118
176



119
142



120
31



121
200



122
90



123
149



124
102



125
105



126
163



127
92



128
47



129
208



130
150



131
153



132
165



133
106



134
55



135
113



136
154



137
79



138
108



139
224



140
166



141
195



142
59



143
169



144
114



145
156



146
87



147
197



148
116



149
170



150
61



151
177



152
91



153
198



154
172



155
120



156
201



157
62



158
143



159
103



160
178



161
93



162
202



163
107



164
180



165
151



166
209



167
94



168
204



169
155



170
210



171
109



172
184



173
115



174
167



175
225



176
157



177
110



178
117



179
212



180
171



181
226



182
216



183
158



184
118



185
173



186
121



187
199



188
179



189
228



190
174



191
122



192
203



193
63



194
181



195
232



196
124



197
205



198
182



199
211



200
185



201
240



202
206



203
95



204
213



205
186



206
227



207
111



208
214



209
188



210
217



211
229



212
159



213
119



214
218



215
230



216
233



217
175



218
123



219
220



220
183



221
234



222
125



223
241



224
207



225
187



226
236



227
126



228
242



229
244



230
189



231
215



232
219



233
231



234
248



235
190



236
221



237
235



238
222



239
237



240
243



241
238



242
245



243
127



244
191



245
246



246
249



247
250



248
252



249
223



250
239



251
251



252
247



253
253



254
254



255
255










Sequence Q14, having a sequence length of 128:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 12, 33, 65, 20, 34, 24, 36, 7, 66, 11, 40, 68, 19, 13, 48, 14, 72, 21, 35, 26, 80, 37, 25, 22, 38, 96, 67, 41, 28, 69, 42, 49, 74, 70, 44, 81, 50, 73, 15, 52, 23, 76, 82, 56, 27, 97, 39, 84, 29, 43, 98, 88, 30, 71, 45, 100, 51, 46, 75, 104, 53, 77, 54, 83, 57, 112, 78, 85, 58, 99, 86, 60, 89, 101, 31, 90, 102, 105, 92, 47, 106, 55, 113, 79, 108, 59, 114, 87, 116, 61, 91, 120, 62, 103, 93, 107, 94, 109, 115, 110, 117, 118, 121, 122, 63, 124, 95, 111, 119, 123, 125, 126, 127]









TABLE Q14







having a sequence length of 128:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
64



10
9



11
6



12
17



13
10



14
18



15
12



16
33



17
65



18
20



19
34



20
24



21
36



22
7



23
66



24
11



25
40



26
68



27
19



28
13



29
48



30
14



31
72



32
21



33
35



34
26



35
80



36
37



37
25



38
22



39
38



40
96



41
67



42
41



43
28



44
69



45
42



46
49



47
74



48
70



49
44



50
81



51
50



52
73



53
15



54
52



55
23



56
76



57
82



58
56



59
27



60
97



61
39



62
84



63
29



64
43



65
98



66
88



67
30



68
71



69
45



70
100



71
51



72
46



73
75



74
104



75
53



76
77



77
54



78
83



79
57



80
112



81
78



82
85



83
58



84
99



85
86



86
60



87
89



88
101



89
31



90
90



91
102



92
105



93
92



94
47



95
106



96
55



97
113



98
79



99
108



100
59



101
114



102
87



103
116



104
61



105
91



106
120



107
62



108
103



109
93



110
107



111
94



112
109



113
115



114
110



115
117



116
118



117
121



118
122



119
63



120
124



121
95



122
111



123
119



124
123



125
125



126
126



127
127










Sequence Q15, having a sequence length of 64:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 9, 6, 17, 10, 18, 12, 33, 20, 34, 24, 36, 7, 11, 40, 19, 13, 48, 14, 21, 35, 26, 37, 25, 22, 38, 41, 28, 42, 49, 44, 50, 15, 52, 23, 56, 27, 39, 29, 43, 30, 45, 51, 46, 53, 54, 57, 58, 60, 31, 47, 55, 59, 61, 62, 63]












TABLE Q15, having a sequence length of 64:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
9



10
6



11
17



12
10



13
18



14
12



15
33



16
20



17
34



18
24



19
36



20
7



21
11



22
40



23
19



24
13



25
48



26
14



27
21



28
35



29
26



30
37



31
25



32
22



33
38



34
41



35
28



36
42



37
49



38
44



39
50



40
15



41
52



42
23



43
56



44
27



45
39



46
29



47
43



48
30



49
45



50
51



51
46



52
53



53
54



54
57



55
58



56
60



57
31



58
47



59
55



60
59



61
61



62
62



63
63










Sequence Z11, having a sequence length of 1024:

    • [0, 1, 2, 7, 3, 8, 11, 24, 4, 10, 13, 28, 16, 33, 35, 76, 5, 12, 14, 32, 19, 38, 47, 80, 22, 46, 42, 87, 57, 95, 101, 160, 6, 17, 21, 40, 23, 45, 51, 89, 29, 55, 59, 96, 71, 108, 113, 175, 34, 61, 74, 111, 79, 120, 129, 186, 86, 131, 141, 208, 146, 218, 236, 327, 9, 18, 26, 54, 30, 58, 70, 103, 36, 75, 62, 114, 83, 123, 135, 193, 44, 73, 85, 130, 91, 138, 145, 214, 99, 148, 162, 228, 174, 242, 256, 357, 53, 88, 97, 144, 109, 154, 169, 239, 118, 170, 185, 250, 195, 269, 282, 382, 133, 191, 211, 273, 216, 283, 301, 403, 233, 307, 322, 419, 337, 434, 460, 582, 15, 25, 31, 72, 39, 78, 81, 134, 48, 84, 92, 143, 100, 153, 157, 238, 56, 93, 102, 155, 112, 168, 182, 252, 122, 183, 192, 264, 213, 279, 297, 395, 64, 106, 119, 173, 124, 184, 198, 274, 142, 209, 217, 285, 232, 306, 317, 418, 156, 225, 240, 311, 251, 333, 339, 432, 270, 348, 370, 453, 386, 472, 511, 583, 68, 121, 137, 201, 152, 215, 231, 309, 161, 234, 244, 326, 257, 338, 356, 447, 180, 253, 265, 346, 284, 366, 384, 478, 293, 388, 406, 494, 424, 518, 532, 641, 197, 275, 288, 373, 312, 394, 409, 506, 336, 415, 433, 526, 454, 535, 567, 671, 355, 440, 461, 552, 470, 577, 591, 695, 509, 598, 613, 690, 629, 714, 743, 830, 20, 37, 41, 90, 49, 94, 104, 167, 50, 105, 115, 176, 126, 194, 202, 295, 63, 116, 127, 205, 139, 212, 223, 296, 147, 222, 237, 321, 254, 335, 342, 431, 66, 136, 149, 207, 164, 226, 241, 334, 172, 248, 258, 344, 268, 364, 377, 468, 171, 266, 277, 363, 292, 385, 397, 495, 314, 411, 425, 517, 439, 531, 555, 663, 77, 159, 165, 246, 179, 262, 276, 358, 187, 281, 287, 383, 302, 402, 414, 515, 235, 298, 313, 405, 328, 422, 438, 528, 350, 443, 464, 550, 481, 576, 593, 686, 261, 324, 345, 430, 362, 452, 466, 568, 380, 475, 487, 581, 512, 605, 619, 707, 407, 510, 519, 614, 529, 630, 609, 721, 560, 660, 672, 749, 677, 779, 794, 846, 82, 177, 181, 291, 227, 305, 316, 410, 247, 320, 329, 427, 349, 445, 463, 570, 259, 347, 361, 446, 372, 467, 483, 585, 389, 489, 505, 601, 527, 617, 640, 725, 294, 365, 376, 482, 396, 500, 521, 610, 426, 522, 533, 638, 561, 627, 667, 751, 451, 546, 574, 661, 586, 676, 688, 770, 606, 693, 692, 790, 722, 801, 813, 877, 323, 387, 412, 523, 444, 534, 554, 647, 465, 569, 578, 673, 597, 679, 691, 777, 484, 589, 611, 687, 620, 694, 723, 802, 646, 729, 740, 816, 760, 834, 844, 905, 516, 615, 636, 724, 666, 726, 756, 821, 670, 753, 772, 840, 786, 853, 870, 924, 680, 780, 798, 859, 808, 873, 865, 930, 828, 885, 893, 946, 909, 954, 963, 984, 27, 43, 52, 98, 60, 117, 128, 199, 65, 132, 140, 204, 151, 220, 224, 330, 67, 150, 158, 219, 166, 263, 271, 354, 188, 272, 290, 381, 304, 398, 413, 525, 69, 163, 178, 267, 190, 289, 299, 392, 200, 308, 318, 416, 332, 435, 449, 536, 210, 325, 341, 442, 359, 462, 473, 564, 367, 469, 490, 588, 493, 600, 616, 745, 107, 189, 196, 303, 206, 319, 331, 429, 229, 343, 351, 457, 369, 477, 488, 572, 245, 353, 375, 471, 391, 492, 497, 594, 404, 498, 504, 618, 545, 631, 656, 752, 260, 390, 400, 503, 421, 520, 524, 624, 437, 544, 557, 645, 580, 664, 674, 773, 456, 566, 587, 675, 607, 685, 709, 787, 635, 712, 730, 803, 741, 819, 836, 903, 110, 203, 221, 340, 243, 352, 371, 480, 255, 378, 393, 499, 408, 508, 513, 621, 280, 401, 420, 514, 436, 541, 553, 642, 455, 562, 579, 669, 595, 681, 700, 774, 300, 428, 448, 556, 474, 575, 573, 682, 485, 590, 599, 696, 625, 710, 718, 805, 507, 608, 633, 715, 643, 735, 742, 822, 659, 750, 764, 841, 789, 855, 871, 925, 315, 459, 476, 592, 496, 604, 626, 713, 539, 634, 650, 738, 653, 744, 758, 833, 547, 651, 658, 755, 683, 763, 783, 852, 704, 788, 797, 860, 812, 878, 888, 933, 563, 689, 698, 775, 719, 791, 800, 867, 731, 810, 823, 884, 837, 894, 907, 949, 766, 825, 842, 897, 857, 911, 916, 961, 868, 921, 929, 966, 940, 974, 983, 1003, 125, 230, 249, 379, 278, 399, 417, 530, 286, 423, 441, 543, 458, 559, 584, 701, 310, 450, 479, 571, 491, 603, 596, 706, 501, 612, 628, 728, 648, 736, 747, 829, 360, 486, 502, 602, 538, 623, 637, 739, 542, 649, 655, 748, 665, 759, 769, 848, 548, 662, 678, 768, 703, 782, 795, 861, 716, 807, 811, 879, 824, 889, 900, 944, 368, 537, 540, 644, 549, 652, 668, 762, 565, 684, 697, 778, 711, 792, 809, 875, 632, 702, 720, 796, 732, 817, 826, 886, 761, 827, 843, 898, 858, 910, 915, 960, 654, 734, 754, 818, 767, 839, 850, 902, 785, 854, 863, 914, 874, 922, 932, 969, 799, 869, 881, 928, 892, 935, 943, 976, 904, 947, 953, 981, 958, 989, 991, 1011, 374, 551, 558, 699, 622, 708, 717, 806, 639, 727, 737, 820, 757, 832, 847, 901, 657, 746, 765, 835, 776, 851, 864, 913, 793, 872, 862, 919, 887, 931, 939, 972, 705, 771, 781, 856, 804, 866, 880, 926, 815, 882, 891, 936, 899, 941, 950, 980, 838, 895, 906, 945, 917, 955, 959, 987, 923, 965, 968, 993, 975, 996, 998, 1008, 733, 784, 814, 883, 831, 890, 896, 942, 845, 908, 912, 952, 920, 956, 967, 990, 849, 918, 927, 964, 938, 970, 971, 997, 948, 977, 979, 999, 985, 1004, 1006, 1016, 876, 934, 937, 973, 951, 978, 982, 1001, 957, 986, 988, 1005, 994, 1007, 1012, 1018, 962, 992, 995, 1009, 1000, 1010, 1013, 1019, 1002, 1014, 1015, 1020, 1017, 1021, 1022, 1023]












Table Z11, having a sequence length of 1024:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
11



7
24



8
4



9
10



10
13



11
28



12
16



13
33



14
35



15
76



16
5



17
12



18
14



19
32



20
19



21
38



22
47



23
80



24
22



25
46



26
42



27
87



28
57



29
95



30
101



31
160



32
6



33
17



34
21



35
40



36
23



37
45



38
51



39
89



40
29



41
55



42
59



43
96



44
71



45
108



46
113



47
175



48
34



49
61



50
74



51
111



52
79



53
120



54
129



55
186



56
86



57
131



58
141



59
208



60
146



61
218



62
236



63
327



64
9



65
18



66
26



67
54



68
30



69
58



70
70



71
103



72
36



73
75



74
62



75
114



76
83



77
123



78
135



79
193



80
44



81
73



82
85



83
130



84
91



85
138



86
145



87
214



88
99



89
148



90
162



91
228



92
174



93
242



94
256



95
357



96
53



97
88



98
97



99
144



100
109



101
154



102
169



103
239



104
118



105
170



106
185



107
250



108
195



109
269



110
282



111
382



112
133



113
191



114
211



115
273



116
216



117
283



118
301



119
403



120
233



121
307



122
322



123
419



124
337



125
434



126
460



127
582



128
15



129
25



130
31



131
72



132
39



133
78



134
81



135
134



136
48



137
84



138
92



139
143



140
100



141
153



142
157



143
238



144
56



145
93



146
102



147
155



148
112



149
168



150
182



151
252



152
122



153
183



154
192



155
264



156
213



157
279



158
297



159
395



160
64



161
106



162
119



163
173



164
124



165
184



166
198



167
274



168
142



169
209



170
217



171
285



172
232



173
306



174
317



175
418



176
156



177
225



178
240



179
311



180
251



181
333



182
339



183
432



184
270



185
348



186
370



187
453



188
386



189
472



190
511



191
583



192
68



193
121



194
137



195
201



196
152



197
215



198
231



199
309



200
161



201
234



202
244



203
326



204
257



205
338



206
356



207
447



208
180



209
253



210
265



211
346



212
284



213
366



214
384



215
478



216
293



217
388



218
406



219
494



220
424



221
518



222
532



223
641



224
197



225
275



226
288



227
373



228
312



229
394



230
409



231
506



232
336



233
415



234
433



235
526



236
454



237
535



238
567



239
671



240
355



241
440



242
461



243
552



244
470



245
577



246
591



247
695



248
509



249
598



250
613



251
690



252
629



253
714



254
743



255
830



256
20



257
37



258
41



259
90



260
49



261
94



262
104



263
167



264
50



265
105



266
115



267
176



268
126



269
194



270
202



271
295



272
63



273
116



274
127



275
205



276
139



277
212



278
223



279
296



280
147



281
222



282
237



283
321



284
254



285
335



286
342



287
431



288
66



289
136



290
149



291
207



292
164



293
226



294
241



295
334



296
172



297
248



298
258



299
344



300
268



301
364



302
377



303
468



304
171



305
266



306
277



307
363



308
292



309
385



310
397



311
495



312
314



313
411



314
425



315
517



316
439



317
531



318
555



319
663



320
77



321
159



322
165



323
246



324
179



325
262



326
276



327
358



328
187



329
281



330
287



331
383



332
302



333
402



334
414



335
515



336
235



337
298



338
313



339
405



340
328



341
422



342
438



343
528



344
350



345
443



346
464



347
550



348
481



349
576



350
593



351
686



352
261



353
324



354
345



355
430



356
362



357
452



358
466



359
568



360
380



361
475



362
487



363
581



364
512



365
605



366
619



367
707



368
407



369
510



370
519



371
614



372
529



373
630



374
609



375
721



376
560



377
660



378
672



379
749



380
677



381
779



382
794



383
846



384
82



385
177



386
181



387
291



388
227



389
305



390
316



391
410



392
247



393
320



394
329



395
427



396
349



397
445



398
463



399
570



400
259



401
347



402
361



403
446



404
372



405
467



406
483



407
585



408
389



409
489



410
505



411
601



412
527



413
617



414
640



415
725



416
294



417
365



418
376



419
482



420
396



421
500



422
521



423
610



424
426



425
522



426
533



427
638



428
561



429
627



430
667



431
751



432
451



433
546



434
574



435
661



436
586



437
676



438
688



439
770



440
606



441
693



442
692



443
790



444
722



445
801



446
813



447
877



448
323



449
387



450
412



451
523



452
444



453
534



454
554



455
647



456
465



457
569



458
578



459
673



460
597



461
679



462
691



463
777



464
484



465
589



466
611



467
687



468
620



469
694



470
723



471
802



472
646



473
729



474
740



475
816



476
760



477
834



478
844



479
905



480
516



481
615



482
636



483
724



484
666



485
726



486
756



487
821



488
670



489
753



490
772



491
840



492
786



493
853



494
870



495
924



496
680



497
780



498
798



499
859



500
808



501
873



502
865



503
930



504
828



505
885



506
893



507
946



508
909



509
954



510
963



511
984



512
27



513
43



514
52



515
98



516
60



517
117



518
128



519
199



520
65



521
132



522
140



523
204



524
151



525
220



526
224



527
330



528
67



529
150



530
158



531
219



532
166



533
263



534
271



535
354



536
188



537
272



538
290



539
381



540
304



541
398



542
413



543
525



544
69



545
163



546
178



547
267



548
190



549
289



550
299



551
392



552
200



553
308



554
318



555
416



556
332



557
435



558
449



559
536



560
210



561
325



562
341



563
442



564
359



565
462



566
473



567
564



568
367



569
469



570
490



571
588



572
493



573
600



574
616



575
745



576
107



577
189



578
196



579
303



580
206



581
319



582
331



583
429



584
229



585
343



586
351



587
457



588
369



589
477



590
488



591
572



592
245



593
353



594
375



595
471



596
391



597
492



598
497



599
594



600
404



601
498



602
504



603
618



604
545



605
631



606
656



607
752



608
260



609
390



610
400



611
503



612
421



613
520



614
524



615
624



616
437



617
544



618
557



619
645



620
580



621
664



622
674



623
773



624
456



625
566



626
587



627
675



628
607



629
685



630
709



631
787



632
635



633
712



634
730



635
803



636
741



637
819



638
836



639
903



640
110



641
203



642
221



643
340



644
243



645
352



646
371



647
480



648
255



649
378



650
393



651
499



652
408



653
508



654
513



655
621



656
280



657
401



658
420



659
514



660
436



661
541



662
553



663
642



664
455



665
562



666
579



667
669



668
595



669
681



670
700



671
774



672
300



673
428



674
448



675
556



676
474



677
575



678
573



679
682



680
485



681
590



682
599



683
696



684
625



685
710



686
718



687
805



688
507



689
608



690
633



691
715



692
643



693
735



694
742



695
822



696
659



697
750



698
764



699
841



700
789



701
855



702
871



703
925



704
315



705
459



706
476



707
592



708
496



709
604



710
626



711
713



712
539



713
634



714
650



715
738



716
653



717
744



718
758



719
833



720
547



721
651



722
658



723
755



724
683



725
763



726
783



727
852



728
704



729
788



730
797



731
860



732
812



733
878



734
888



735
933



736
563



737
689



738
698



739
775



740
719



741
791



742
800



743
867



744
731



745
810



746
823



747
884



748
837



749
894



750
907



751
949



752
766



753
825



754
842



755
897



756
857



757
911



758
916



759
961



760
868



761
921



762
929



763
966



764
940



765
974



766
983



767
1003



768
125



769
230



770
249



771
379



772
278



773
399



774
417



775
530



776
286



777
423



778
441



779
543



780
458



781
559



782
584



783
701



784
310



785
450



786
479



787
571



788
491



789
603



790
596



791
706



792
501



793
612



794
628



795
728



796
648



797
736



798
747



799
829



800
360



801
486



802
502



803
602



804
538



805
623



806
637



807
739



808
542



809
649



810
655



811
748



812
665



813
759



814
769



815
848



816
548



817
662



818
678



819
768



820
703



821
782



822
795



823
861



824
716



825
807



826
811



827
879



828
824



829
889



830
900



831
944



832
368



833
537



834
540



835
644



836
549



837
652



838
668



839
762



840
565



841
684



842
697



843
778



844
711



845
792



846
809



847
875



848
632



849
702



850
720



851
796



852
732



853
817



854
826



855
886



856
761



857
827



858
843



859
898



860
858



861
910



862
915



863
960



864
654



865
734



866
754



867
818



868
767



869
839



870
850



871
902



872
785



873
854



874
863



875
914



876
874



877
922



878
932



879
969



880
799



881
869



882
881



883
928



884
892



885
935



886
943



887
976



888
904



889
947



890
953



891
981



892
958



893
989



894
991



895
1011



896
374



897
551



898
558



899
699



900
622



901
708



902
717



903
806



904
639



905
727



906
737



907
820



908
757



909
832



910
847



911
901



912
657



913
746



914
765



915
835



916
776



917
851



918
864



919
913



920
793



921
872



922
862



923
919



924
887



925
931



926
939



927
972



928
705



929
771



930
781



931
856



932
804



933
866



934
880



935
926



936
815



937
882



938
891



939
936



940
899



941
941



942
950



943
980



944
838



945
895



946
906



947
945



948
917



949
955



950
959



951
987



952
923



953
965



954
968



955
993



956
975



957
996



958
998



959
1008



960
733



961
784



962
814



963
883



964
831



965
890



966
896



967
942



968
845



969
908



970
912



971
952



972
920



973
956



974
967



975
990



976
849



977
918



978
927



979
964



980
938



981
970



982
971



983
997



984
948



985
977



986
979



987
999



988
985



989
1004



990
1006



991
1016



992
876



993
934



994
937



995
973



996
951



997
978



998
982



999
1001



1000
957



1001
986



1002
988



1003
1005



1004
994



1005
1007



1006
1012



1007
1018



1008
962



1009
992



1010
995



1011
1009



1012
1000



1013
1010



1014
1013



1015
1019



1016
1002



1017
1014



1018
1015



1019
1020



1020
1017



1021
1021



1022
1022



1023
1023










Sequence Z12, having a sequence length of 512:

    • [0, 1, 2, 7, 3, 8, 11, 24, 4, 10, 13, 27, 16, 32, 34, 69, 5, 12, 14, 31, 19, 37, 45, 73, 22, 44, 41, 80, 54, 88, 93, 142, 6, 17, 21, 39, 23, 43, 49, 82, 28, 52, 56, 89, 64, 99, 103, 155, 33, 57, 67, 101, 72, 109, 116, 165, 79, 118, 126, 178, 131, 187, 199, 266, 9, 18, 26, 51, 29, 55, 63, 95, 35, 68, 58, 104, 76, 112, 121, 169, 42, 66, 78, 117, 84, 124, 130, 183, 91, 133, 144, 193, 154, 205, 215, 286, 50, 81, 90, 129, 100, 137, 149, 202, 107, 150, 164, 210, 171, 225, 234, 300, 119, 167, 180, 227, 185, 235, 248, 313, 196, 252, 262, 324, 273, 334, 347, 407, 15, 25, 30, 65, 38, 71, 74, 120, 46, 77, 85, 128, 92, 136, 140, 201, 53, 86, 94, 138, 102, 148, 161, 212, 111, 162, 168, 221, 182, 232, 246, 309, 60, 98, 108, 153, 113, 163, 173, 228, 127, 179, 186, 237, 195, 251, 259, 323, 139, 190, 203, 254, 211, 269, 275, 332, 226, 281, 294, 345, 304, 356, 372, 408, 62, 110, 123, 174, 135, 184, 194, 253, 143, 197, 206, 265, 216, 274, 285, 342, 159, 213, 222, 279, 236, 293, 302, 358, 242, 306, 315, 365, 326, 377, 387, 434, 172, 229, 239, 296, 255, 308, 317, 369, 272, 322, 333, 382, 346, 390, 398, 443, 284, 337, 348, 393, 355, 404, 412, 458, 370, 415, 422, 453, 429, 460, 469, 491, 20, 36, 40, 83, 47, 87, 96, 147, 48, 97, 105, 156, 114, 170, 175, 244, 59, 106, 115, 176, 125, 181, 189, 245, 132, 188, 200, 261, 214, 271, 276, 331, 61, 122, 134, 177, 145, 191, 204, 270, 152, 209, 217, 277, 224, 291, 298, 354, 151, 223, 231, 290, 241, 303, 311, 366, 257, 319, 327, 376, 336, 386, 395, 439, 70, 141, 146, 207, 158, 220, 230, 287, 166, 233, 238, 301, 249, 312, 321, 374, 198, 247, 256, 314, 267, 325, 335, 384, 283, 338, 350, 392, 359, 403, 413, 450, 219, 264, 278, 330, 289, 344, 352, 399, 299, 357, 363, 406, 373, 417, 426, 459, 316, 371, 378, 423, 385, 430, 419, 461, 396, 437, 444, 470, 447, 478, 482, 495, 75, 157, 160, 240, 192, 250, 258, 318, 208, 260, 268, 329, 282, 340, 349, 401, 218, 280, 288, 341, 295, 353, 361, 409, 307, 364, 368, 416, 383, 425, 433, 465, 243, 292, 297, 360, 310, 367, 379, 420, 328, 380, 388, 432, 397, 428, 441, 471, 343, 391, 402, 438, 410, 446, 452, 475, 418, 456, 455, 481, 462, 484, 487, 501, 263, 305, 320, 381, 339, 389, 394, 436, 351, 400, 405, 445, 414, 448, 454, 477, 362, 411, 421, 451, 427, 457, 463, 485, 435, 467, 468, 488, 474, 492, 494, 504, 375, 424, 431, 464, 440, 466, 473, 489, 442, 472, 476, 493, 480, 496, 499, 506, 449, 479, 483, 497, 486, 500, 498, 507, 490, 502, 503, 508, 505, 509, 510, 511]












TABLE Z12, having a sequence length of 512:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
11



7
24



8
4



9
10



10
13



11
27



12
16



13
32



14
34



15
69



16
5



17
12



18
14



19
31



20
19



21
37



22
45



23
73



24
22



25
44



26
41



27
80



28
54



29
88



30
93



31
142



32
6



33
17



34
21



35
39



36
23



37
43



38
49



39
82



40
28



41
52



42
56



43
89



44
64



45
99



46
103



47
155



48
33



49
57



50
67



51
101



52
72



53
109



54
116



55
165



56
79



57
118



58
126



59
178



60
131



61
187



62
199



63
266



64
9



65
18



66
26



67
51



68
29



69
55



70
63



71
95



72
35



73
68



74
58



75
104



76
76



77
112



78
121



79
169



80
42



81
66



82
78



83
117



84
84



85
124



86
130



87
183



88
91



89
133



90
144



91
193



92
154



93
205



94
215



95
286



96
50



97
81



98
90



99
129



100
100



101
137



102
149



103
202



104
107



105
150



106
164



107
210



108
171



109
225



110
234



111
300



112
119



113
167



114
180



115
227



116
185



117
235



118
248



119
313



120
196



121
252



122
262



123
324



124
273



125
334



126
347



127
407



128
15



129
25



130
30



131
65



132
38



133
71



134
74



135
120



136
46



137
77



138
85



139
128



140
92



141
136



142
140



143
201



144
53



145
86



146
94



147
138



148
102



149
148



150
161



151
212



152
111



153
162



154
168



155
221



156
182



157
232



158
246



159
309



160
60



161
98



162
108



163
153



164
113



165
163



166
173



167
228



168
127



169
179



170
186



171
237



172
195



173
251



174
259



175
323



176
139



177
190



178
203



179
254



180
211



181
269



182
275



183
332



184
226



185
281



186
294



187
345



188
304



189
356



190
372



191
408



192
62



193
110



194
123



195
174



196
135



197
184



198
194



199
253



200
143



201
197



202
206



203
265



204
216



205
274



206
285



207
342



208
159



209
213



210
222



211
279



212
236



213
293



214
302



215
358



216
242



217
306



218
315



219
365



220
326



221
377



222
387



223
434



224
172



225
229



226
239



227
296



228
255



229
308



230
317



231
369



232
272



233
322



234
333



235
382



236
346



237
390



238
398



239
443



240
284



241
337



242
348



243
393



244
355



245
404



246
412



247
458



248
370



249
415



250
422



251
453



252
429



253
460



254
469



255
491



256
20



257
36



258
40



259
83



260
47



261
87



262
96



263
147



264
48



265
97



266
105



267
156



268
114



269
170



270
175



271
244



272
59



273
106



274
115



275
176



276
125



277
181



278
189



279
245



280
132



281
188



282
200



283
261



284
214



285
271



286
276



287
331



288
61



289
122



290
134



291
177



292
145



293
191



294
204



295
270



296
152



297
209



298
217



299
277



300
224



301
291



302
298



303
354



304
151



305
223



306
231



307
290



308
241



309
303



310
311



311
366



312
257



313
319



314
327



315
376



316
336



317
386



318
395



319
439



320
70



321
141



322
146



323
207



324
158



325
220



326
230



327
287



328
166



329
233



330
238



331
301



332
249



333
312



334
321



335
374



336
198



337
247



338
256



339
314



340
267



341
325



342
335



343
384



344
283



345
338



346
350



347
392



348
359



349
403



350
413



351
450



352
219



353
264



354
278



355
330



356
289



357
344



358
352



359
399



360
299



361
357



362
363



363
406



364
373



365
417



366
426



367
459



368
316



369
371



370
378



371
423



372
385



373
430



374
419



375
461



376
396



377
437



378
444



379
470



380
447



381
478



382
482



383
495



384
75



385
157



386
160



387
240



388
192



389
250



390
258



391
318



392
208



393
260



394
268



395
329



396
282



397
340



398
349



399
401



400
218



401
280



402
288



403
341



404
295



405
353



406
361



407
409



408
307



409
364



410
368



411
416



412
383



413
425



414
433



415
465



416
243



417
292



418
297



419
360



420
310



421
367



422
379



423
420



424
328



425
380



426
388



427
432



428
397



429
428



430
441



431
471



432
343



433
391



434
402



435
438



436
410



437
446



438
452



439
475



440
418



441
456



442
455



443
481



444
462



445
484



446
487



447
501



448
263



449
305



450
320



451
381



452
339



453
389



454
394



455
436



456
351



457
400



458
405



459
445



460
414



461
448



462
454



463
477



464
362



465
411



466
421



467
451



468
427



469
457



470
463



471
485



472
435



473
467



474
468



475
488



476
474



477
492



478
494



479
504



480
375



481
424



482
431



483
464



484
440



485
466



486
473



487
489



488
442



489
472



490
476



491
493



492
480



493
496



494
499



495
506



496
449



497
479



498
483



499
497



500
486



501
500



502
498



503
507



504
490



505
502



506
503



507
508



508
505



509
509



510
510



511
511










Sequence Z13, having a sequence length of 256:

    • [0, 1, 2, 7, 3, 8, 11, 23, 4, 10, 13, 26, 16, 31, 33, 62, 5, 12, 14, 30, 19, 35, 42, 65, 21, 41, 38, 71, 49, 77, 82, 120, 6, 17, 20, 37, 22, 40, 44, 73, 27, 47, 51, 78, 57, 86, 90, 128, 32, 52, 60, 88, 64, 94, 99, 134, 70, 101, 107, 142, 112, 150, 157, 193, 9, 18, 25, 46, 28, 50, 56, 84, 34, 61, 53, 91, 67, 97, 104, 137, 39, 59, 69, 100, 74, 106, 111, 146, 80, 113, 122, 152, 127, 161, 167, 203, 45, 72, 79, 110, 87, 116, 124, 159, 92, 125, 133, 163, 138, 171, 177, 207, 102, 135, 144, 173, 148, 178, 184, 213, 155, 186, 191, 218, 196, 222, 227, 243, 15, 24, 29, 58, 36, 63, 66, 103, 43, 68, 75, 109, 81, 115, 119, 158, 48, 76, 83, 117, 89, 123, 130, 165, 96, 131, 136, 169, 145, 176, 183, 212, 54, 85, 93, 126, 98, 132, 140, 174, 108, 143, 149, 180, 154, 185, 190, 217, 118, 151, 160, 188, 164, 194, 198, 220, 172, 200, 205, 225, 209, 230, 235, 244, 55, 95, 105, 141, 114, 147, 153, 187, 121, 156, 162, 192, 168, 197, 202, 224, 129, 166, 170, 199, 179, 204, 208, 231, 182, 210, 214, 232, 219, 236, 238, 249, 139, 175, 181, 206, 189, 211, 215, 233, 195, 216, 221, 237, 226, 239, 241, 250, 201, 223, 228, 240, 229, 242, 245, 252, 234, 246, 247, 251, 248, 253, 254, 255]









TABLE Z13







having a sequence length of 256:










Polarized
Reliability



channel
or sequence



sequence
number of



number
reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
11



7
23



8
4



9
10



10
13



11
26



12
16



13
31



14
33



15
62



16
5



17
12



18
14



19
30



20
19



21
35



22
42



23
65



24
21



25
41



26
38



27
71



28
49



29
77



30
82



31
120



32
6



33
17



34
20



35
37



36
22



37
40



38
44



39
73



40
27



41
47



42
51



43
78



44
57



45
86



46
90



47
128



48
32



49
52



50
60



51
88



52
64



53
94



54
99



55
134



56
70



57
101



58
107



59
142



60
112



61
150



62
157



63
193



64
9



65
18



66
25



67
46



68
28



69
50



70
56



71
84



72
34



73
61



74
53



75
91



76
67



77
97



78
104



79
137



80
39



81
59



82
69



83
100



84
74



85
106



86
111



87
146



88
80



89
113



90
122



91
152



92
127



93
161



94
167



95
203



96
45



97
72



98
79



99
110



100
87



101
116



102
124



103
159



104
92



105
125



106
133



107
163



108
138



109
171



110
177



111
207



112
102



113
135



114
144



115
173



116
148



117
178



118
184



119
213



120
155



121
186



122
191



123
218



124
196



125
222



126
227



127
243



128
15



129
24



130
29



131
58



132
36



133
63



134
66



135
103



136
43



137
68



138
75



139
109



140
81



141
115



142
119



143
158



144
48



145
76



146
83



147
117



148
89



149
123



150
130



151
165



152
96



153
131



154
136



155
169



156
145



157
176



158
183



159
212



160
54



161
85



162
93



163
126



164
98



165
132



166
140



167
174



168
108



169
143



170
149



171
180



172
154



173
185



174
190



175
217



176
118



177
151



178
160



179
188



180
164



181
194



182
198



183
220



184
172



185
200



186
205



187
225



188
209



189
230



190
235



191
244



192
55



193
95



194
105



195
141



196
114



197
147



198
153



199
187



200
121



201
156



202
162



203
192



204
168



205
197



206
202



207
224



208
129



209
166



210
170



211
199



212
179



213
204



214
208



215
231



216
182



217
210



218
214



219
232



220
219



221
236



222
238



223
249



224
139



225
175



226
181



227
206



228
189



229
211



230
215



231
233



232
195



233
216



234
221



235
237



236
226



237
239



238
241



239
250



240
201



241
223



242
228



243
240



244
229



245
242



246
245



247
252



248
234



249
246



250
247



251
251



252
248



253
253



254
254



255
255










Sequence Z14, having a sequence length of 128:

    • [0, 1, 2, 7, 3, 8, 11, 22, 4, 10, 13, 24, 15, 28, 30, 53, 5, 12, 14, 27, 18, 32, 38, 55, 20, 37, 34, 59, 43, 63, 67, 89, 6, 16, 19, 33, 21, 36, 39, 61, 25, 42, 45, 64, 49, 69, 72, 94, 29, 46, 51, 71, 54, 75, 77, 96, 58, 79, 83, 100, 86, 104, 107, 119, 9, 17, 23, 41, 26, 44, 48, 68, 31, 52, 47, 73, 56, 76, 81, 98, 35, 50, 57, 78, 62, 82, 85, 102, 66, 87, 90, 105, 93, 109, 111, 121, 40, 60, 65, 84, 70, 88, 91, 108, 74, 92, 95, 110, 99, 112, 114, 122, 80, 97, 101, 113, 103, 115, 116, 123, 106, 117, 118, 124, 120, 125, 126, 127]









TABLE Z14







having a sequence length of 128:










Polarized
Reliability or



channel
sequence



sequence
number of



number
reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
11



7
22



8
4



9
10



10
13



11
24



12
15



13
28



14
30



15
53



16
5



17
12



18
14



19
27



20
18



21
32



22
38



23
55



24
20



25
37



26
34



27
59



28
43



29
63



30
67



31
89



32
6



33
16



34
19



35
33



36
21



37
36



38
39



39
61



40
25



41
42



42
45



43
64



44
49



45
69



46
72



47
94



48
29



49
46



50
51



51
71



52
54



53
75



54
77



55
96



56
58



57
79



58
83



59
100



60
86



61
104



62
107



63
119



64
9



65
17



66
23



67
41



68
26



69
44



70
48



71
68



72
31



73
52



74
47



75
73



76
56



77
76



78
81



79
98



80
35



81
50



82
57



83
78



84
62



85
82



86
85



87
102



88
66



89
87



90
90



91
105



92
93



93
109



94
111



95
121



96
40



97
60



98
65



99
84



100
70



101
88



102
91



103
108



104
74



105
92



106
95



107
110



108
99



109
112



110
114



111
122



112
80



113
97



114
101



115
113



116
103



117
115



118
116



119
123



120
106



121
117



122
118



123
124



124
120



125
125



126
126



127
127










Sequence Z, having a sequence length of 64:

    • [0, 1, 2, 7, 3, 8, 10, 20, 4, 9, 12, 21, 14, 24, 26, 40, 5, 11, 13, 23, 16, 27, 32, 42, 18, 31, 29, 44, 35, 46, 48, 57, 6, 15, 17, 28, 19, 30, 33, 45, 22, 34, 36, 47, 38, 49, 51, 58, 25, 37, 39, 50, 41, 52, 53, 59, 43, 54, 55, 60, 56, 61, 62, 63]












Table Z15, having a sequence length of 64:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
10



7
20



8
4



9
9



10
12



11
21



12
14



13
24



14
26



15
40



16
5



17
11



18
13



19
23



20
16



21
27



22
32



23
42



24
18



25
31



26
29



27
44



28
35



29
46



30
48



31
57



32
6



33
15



34
17



35
28



36
19



37
30



38
33



39
45



40
22



41
34



42
36



43
47



44
38



45
49



46
51



47
58



48
25



49
37



50
39



51
50



52
41



53
52



54
53



55
59



56
43



57
54



58
55



59
60



60
56



61
61



62
62



63
63










Fourth group of sequences (a criterion that considers a performance balance under partial-order (partial-order) constraints).


Sequence Q16, having a sequence length of 1024:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 65, 20, 256, 34, 24, 36, 7, 129, 66, 512, 11, 40, 68, 130, 19, 13, 48, 14, 72, 257, 21, 132, 35, 258, 22, 80, 136, 513, 25, 37, 260, 264, 26, 96, 514, 38, 67, 41, 144, 28, 69, 516, 42, 272, 49, 70, 520, 160, 44, 131, 73, 288, 528, 192, 50, 74, 544, 52, 15, 133, 320, 81, 23, 134, 384, 76, 56, 259, 82, 137, 27, 97, 39, 84, 138, 145, 261, 29, 43, 98, 515, 88, 140, 30, 146, 71, 262, 265, 161, 576, 45, 100, 640, 51, 148, 46, 75, 266, 273, 517, 104, 162, 53, 193, 152, 77, 164, 768, 268, 274, 518, 54, 83, 57, 521, 112, 135, 78, 289, 194, 85, 276, 522, 58, 168, 139, 99, 86, 60, 280, 89, 290, 529, 524, 196, 141, 101, 147, 176, 142, 530, 321, 90, 200, 31, 545, 292, 322, 532, 263, 149, 102, 105, 296, 304, 163, 92, 47, 267, 150, 208, 385, 546, 386, 324, 106, 153, 165, 55, 328, 536, 577, 548, 113, 154, 79, 269, 108, 578, 224, 166, 519, 552, 195, 270, 641, 523, 275, 580, 291, 169, 59, 560, 114, 277, 156, 87, 197, 116, 170, 61, 531, 525, 642, 281, 278, 526, 177, 293, 388, 91, 584, 769, 198, 172, 120, 201, 336, 62, 282, 143, 103, 178, 294, 93, 644, 202, 592, 323, 392, 297, 770, 107, 180, 151, 209, 284, 648, 94, 204, 298, 400, 352, 608, 325, 533, 155, 210, 305, 547, 300, 109, 184, 115, 534, 167, 225, 537, 326, 306, 772, 157, 656, 329, 110, 117, 212, 171, 330, 226, 549, 776, 538, 387, 308, 216, 416, 271, 279, 158, 337, 550, 672, 118, 332, 579, 540, 389, 173, 121, 553, 199, 784, 179, 228, 338, 390, 122, 554, 448, 312, 581, 393, 283, 704, 174, 394, 181, 340, 203, 353, 561, 527, 582, 556, 63, 295, 285, 232, 124, 286, 562, 205, 182, 643, 585, 299, 354, 211, 401, 185, 396, 344, 586, 645, 593, 535, 240, 206, 95, 327, 564, 800, 402, 356, 307, 301, 417, 213, 186, 539, 404, 227, 594, 568, 771, 418, 649, 302, 832, 551, 111, 896, 360, 588, 609, 331, 214, 309, 188, 449, 217, 646, 408, 229, 541, 159, 420, 596, 650, 773, 310, 333, 119, 657, 658, 610, 368, 339, 391, 313, 218, 334, 542, 230, 233, 774, 612, 175, 123, 652, 600, 450, 583, 341, 220, 555, 314, 557, 424, 395, 777, 673, 355, 287, 183, 234, 125, 616, 342, 563, 778, 660, 558, 452, 674, 397, 785, 432, 316, 345, 241, 207, 403, 357, 187, 587, 565, 664, 624, 780, 236, 126, 242, 398, 705, 346, 456, 358, 405, 303, 569, 189, 595, 215, 566, 676, 361, 706, 589, 244, 786, 647, 348, 419, 406, 464, 801, 590, 362, 570, 409, 680, 597, 788, 572, 219, 311, 708, 598, 601, 651, 421, 792, 802, 611, 602, 369, 190, 688, 653, 248, 231, 410, 364, 654, 659, 335, 480, 315, 221, 613, 422, 370, 425, 235, 451, 543, 614, 412, 343, 222, 775, 317, 372, 426, 453, 237, 559, 833, 804, 712, 834, 661, 808, 779, 617, 604, 433, 720, 816, 836, 347, 897, 243, 662, 454, 318, 675, 618, 898, 781, 376, 428, 665, 736, 567, 840, 625, 238, 359, 457, 399, 787, 677, 434, 349, 458, 678, 245, 666, 363, 591, 127, 620, 407, 782, 436, 465, 626, 571, 246, 681, 350, 707, 460, 599, 668, 789, 249, 411, 682, 573, 365, 803, 790, 709, 440, 466, 793, 574, 371, 423, 689, 603, 366, 628, 250, 413, 468, 655, 481, 900, 805, 191, 373, 615, 684, 427, 710, 794, 605, 414, 252, 713, 374, 848, 690, 632, 806, 482, 429, 904, 809, 455, 223, 663, 835, 692, 619, 472, 714, 796, 721, 837, 716, 864, 810, 606, 912, 722, 696, 377, 817, 435, 484, 621, 812, 319, 430, 838, 667, 239, 378, 459, 437, 622, 627, 488, 380, 818, 461, 496, 669, 679, 724, 841, 629, 351, 467, 438, 737, 247, 462, 441, 442, 469, 251, 683, 842, 738, 899, 670, 783, 849, 820, 728, 928, 791, 367, 901, 630, 685, 844, 633, 711, 253, 691, 824, 902, 686, 740, 850, 375, 444, 470, 483, 905, 415, 485, 795, 473, 634, 744, 852, 960, 865, 693, 797, 906, 715, 807, 474, 636, 694, 254, 717, 575, 811, 697, 866, 798, 379, 431, 913, 607, 489, 723, 486, 908, 718, 813, 476, 856, 839, 725, 698, 914, 752, 868, 819, 814, 439, 929, 490, 623, 671, 739, 916, 463, 843, 381, 497, 930, 821, 726, 961, 872, 492, 631, 729, 700, 443, 741, 845, 920, 382, 822, 851, 730, 498, 880, 742, 445, 471, 635, 932, 687, 903, 825, 500, 846, 745, 826, 732, 446, 962, 936, 475, 853, 867, 637, 907, 487, 695, 746, 828, 753, 854, 857, 504, 799, 909, 719, 638, 915, 477, 255, 964, 699, 748, 869, 944, 491, 754, 910, 858, 917, 478, 968, 870, 815, 383, 727, 493, 873, 701, 931, 756, 860, 499, 731, 823, 702, 918, 921, 874, 494, 976, 760, 933, 881, 501, 743, 922, 876, 847, 934, 827, 733, 882, 502, 447, 992, 937, 963, 747, 505, 855, 924, 734, 829, 938, 884, 506, 965, 749, 945, 966, 755, 859, 940, 830, 911, 871, 888, 479, 946, 750, 969, 861, 757, 970, 919, 875, 758, 508, 862, 639, 948, 977, 923, 972, 761, 877, 952, 495, 703, 935, 978, 883, 762, 503, 925, 878, 735, 993, 885, 939, 994, 980, 926, 764, 941, 967, 886, 831, 947, 507, 889, 984, 751, 942, 996, 971, 890, 509, 949, 973, 1000, 892, 950, 863, 759, 1008, 510, 979, 953, 763, 974, 954, 879, 981, 982, 927, 995, 765, 956, 887, 985, 997, 986, 943, 891, 998, 766, 511, 988, 1001, 951, 1002, 893, 975, 894, 1009, 955, 1004, 1010, 957, 983, 958, 987, 1012, 999, 1016, 767, 989, 1003, 990, 1005, 895, 1011, 1013, 959, 1006, 1014, 1017, 1018, 991, 1020, 1007, 1015, 1019, 1021, 1022, 1023]












Table Q16, having a sequence length of 1024:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
64



10
9



11
6



12
17



13
10



14
18



15
128



16
12



17
33



18
65



19
20



20
256



21
34



22
24



23
36



24
7



25
129



26
66



27
512



28
11



29
40



30
68



31
130



32
19



33
13



34
48



35
14



36
72



37
257



38
21



39
132



40
35



41
258



42
22



43
80



44
136



45
513



46
25



47
37



48
260



49
264



50
26



51
96



52
514



53
38



54
67



55
41



56
144



57
28



58
69



59
516



60
42



61
272



62
49



63
70



64
520



65
160



66
44



67
131



68
73



69
288



70
528



71
192



72
50



73
74



74
544



75
52



76
15



77
133



78
320



79
81



80
23



81
134



82
384



83
76



84
56



85
259



86
82



87
137



88
27



89
97



90
39



91
84



92
138



93
145



94
261



95
29



96
43



97
98



98
515



99
88



100
140



101
30



102
146



103
71



104
262



105
265



106
161



107
576



108
45



109
100



110
640



111
51



112
148



113
46



114
75



115
266



116
273



117
517



118
104



119
162



120
53



121
193



122
152



123
77



124
164



125
768



126
268



127
274



128
518



129
54



130
83



131
57



132
521



133
112



134
135



135
78



136
289



137
194



138
85



139
276



140
522



141
58



142
168



143
139



144
99



145
86



146
60



147
280



148
89



149
290



150
529



151
524



152
196



153
141



154
101



155
147



156
176



157
142



158
530



159
321



160
90



161
200



162
31



163
545



164
292



165
322



166
532



167
263



168
149



169
102



170
105



171
296



172
304



173
163



174
92



175
47



176
267



177
150



178
208



179
385



180
546



181
386



182
324



183
106



184
153



185
165



186
55



187
328



188
536



189
577



190
548



191
113



192
154



193
79



194
269



195
108



196
578



197
224



198
166



199
519



200
552



201
195



202
270



203
641



204
523



205
275



206
580



207
291



208
169



209
59



210
560



211
114



212
277



213
156



214
87



215
197



216
116



217
170



218
61



219
531



220
525



221
642



222
281



223
278



224
526



225
177



226
293



227
388



228
91



229
584



230
769



231
198



232
172



233
120



234
201



235
336



236
62



237
282



238
143



239
103



240
178



241
294



242
93



243
644



244
202



245
592



246
323



247
392



248
297



249
770



250
107



251
180



252
151



253
209



254
284



255
648



256
94



257
204



258
298



259
400



260
352



261
608



262
325



263
533



264
155



265
210



266
305



267
547



268
300



269
109



270
184



271
115



272
534



273
167



274
225



275
537



276
326



277
306



278
772



279
157



280
656



281
329



282
110



283
117



284
212



285
171



286
330



287
226



288
549



289
776



290
538



291
387



292
308



293
216



294
416



295
271



296
279



297
158



298
337



299
550



300
672



301
118



302
332



303
579



304
540



305
389



306
173



307
121



308
553



309
199



310
784



311
179



312
228



313
338



314
390



315
122



316
554



317
448



318
312



319
581



320
393



321
283



322
704



323
174



324
394



325
181



326
340



327
203



328
353



329
561



330
527



331
582



332
556



333
63



334
295



335
285



336
232



337
124



338
286



339
562



340
205



341
182



342
643



343
585



344
299



345
354



346
211



347
401



348
185



349
396



350
344



351
586



352
645



353
593



354
535



355
240



356
206



357
95



358
327



359
564



360
800



361
402



362
356



363
307



364
301



365
417



366
213



367
186



368
539



369
404



370
227



371
594



372
568



373
771



374
418



375
649



376
302



377
832



378
551



379
111



380
896



381
360



382
588



383
609



384
331



385
214



386
309



387
188



388
449



389
217



390
646



391
408



392
229



393
541



394
159



395
420



396
596



397
650



398
773



399
310



400
333



401
119



402
657



403
658



404
610



405
368



406
339



407
391



408
313



409
218



410
334



411
542



412
230



413
233



414
774



415
612



416
175



417
123



418
652



419
600



420
450



421
583



422
341



423
220



424
555



425
314



426
557



427
424



428
395



429
777



430
673



431
355



432
287



433
183



434
234



435
125



436
616



437
342



438
563



439
778



440
660



441
558



442
452



443
674



444
397



445
785



446
432



447
316



448
345



449
241



450
207



451
403



452
357



453
187



454
587



455
565



456
664



457
624



458
780



459
236



460
126



461
242



462
398



463
705



464
346



465
456



466
358



467
405



468
303



469
569



470
189



471
595



472
215



473
566



474
676



475
361



476
706



477
589



478
244



479
786



480
647



481
348



482
419



483
406



484
464



485
801



486
590



487
362



488
570



489
409



490
680



491
597



492
788



493
572



494
219



495
311



496
708



497
598



498
601



499
651



500
421



501
792



502
802



503
611



504
602



505
369



506
190



507
688



508
653



509
248



510
231



511
410



512
364



513
654



514
659



515
335



516
480



517
315



518
221



519
613



520
422



521
370



522
425



523
235



524
451



525
543



526
614



527
412



528
343



529
222



530
775



531
317



532
372



533
426



534
453



535
237



536
559



537
833



538
804



539
712



540
834



541
661



542
808



543
779



544
617



545
604



546
433



547
720



548
816



549
836



550
347



551
897



552
243



553
662



554
454



555
318



556
675



557
618



558
898



559
781



560
376



561
428



562
665



563
736



564
567



565
840



566
625



567
238



568
359



569
457



570
399



571
787



572
677



573
434



574
349



575
458



576
678



577
245



578
666



579
363



580
591



581
127



582
620



583
407



584
782



585
436



586
465



587
626



588
571



589
246



590
681



591
350



592
707



593
460



594
599



595
668



596
789



597
249



598
411



599
682



600
573



601
365



602
803



603
790



604
709



605
440



606
466



607
793



608
574



609
371



610
423



611
689



612
603



613
366



614
628



615
250



616
413



617
468



618
655



619
481



620
900



621
805



622
191



623
373



624
615



625
684



626
427



627
710



628
794



629
605



630
414



631
252



632
713



633
374



634
848



635
690



636
632



637
806



638
482



639
429



640
904



641
809



642
455



643
223



644
663



645
835



646
692



647
619



648
472



649
714



650
796



651
721



652
837



653
716



654
864



655
810



656
606



657
912



658
722



659
696



660
377



661
817



662
435



663
484



664
621



665
812



666
319



667
430



668
838



669
667



670
239



671
378



672
459



673
437



674
622



675
627



676
488



677
380



678
818



679
461



680
496



681
669



682
679



683
724



684
841



685
629



686
351



687
467



688
438



689
737



690
247



691
462



692
441



693
442



694
469



695
251



696
683



697
842



698
738



699
899



700
670



701
783



702
849



703
820



704
728



705
928



706
791



707
367



708
901



709
630



710
685



711
844



712
633



713
711



714
253



715
691



716
824



717
902



718
686



719
740



720
850



721
375



722
444



723
470



724
483



725
905



726
415



727
485



728
795



729
473



730
634



731
744



732
852



733
960



734
865



735
693



736
797



737
906



738
715



739
807



740
474



741
636



742
694



743
254



744
717



745
575



746
811



747
697



748
866



749
798



750
379



751
431



752
913



753
607



754
489



755
723



756
486



757
908



758
718



759
813



760
476



761
856



762
839



763
725



764
698



765
914



766
752



767
868



768
819



769
814



770
439



771
929



772
490



773
623



774
671



775
739



776
916



777
463



778
843



779
381



780
497



781
930



782
821



783
726



784
961



785
872



786
492



787
631



788
729



789
700



790
443



791
741



792
845



793
920



794
382



795
822



796
851



797
730



798
498



799
880



800
742



801
445



802
471



803
635



804
932



805
687



806
903



807
825



808
500



809
846



810
745



811
826



812
732



813
446



814
962



815
936



816
475



817
853



818
867



819
637



820
907



821
487



822
695



823
746



824
828



825
753



826
854



827
857



828
504



829
799



830
909



831
719



832
638



833
915



834
477



835
255



836
964



837
699



838
748



839
869



840
944



841
491



842
754



843
910



844
858



845
917



846
478



847
968



848
870



849
815



850
383



851
727



852
493



853
873



854
701



855
931



856
756



857
860



858
499



859
731



860
823



861
702



862
918



863
921



864
874



865
494



866
976



867
760



868
933



869
881



870
501



871
743



872
922



873
876



874
847



875
934



876
827



877
733



878
882



879
502



880
447



881
992



882
937



883
963



884
747



885
505



886
855



887
924



888
734



889
829



890
938



891
884



892
506



893
965



894
749



895
945



896
966



897
755



898
859



899
940



900
830



901
911



902
871



903
888



904
479



905
946



906
750



907
969



908
861



909
757



910
970



911
919



912
875



913
758



914
508



915
862



916
639



917
948



918
977



919
923



920
972



921
761



922
877



923
952



924
495



925
703



926
935



927
978



928
883



929
762



930
503



931
925



932
878



933
735



934
993



935
885



936
939



937
994



938
980



939
926



940
764



941
941



942
967



943
886



944
831



945
947



946
507



947
889



948
984



949
751



950
942



951
996



952
971



953
890



954
509



955
949



956
973



957
1000



958
892



959
950



960
863



961
759



962
1008



963
510



964
979



965
953



966
763



967
974



968
954



969
879



970
981



971
982



972
927



973
995



974
765



975
956



976
887



977
985



978
997



979
986



980
943



981
891



982
998



983
766



984
511



985
988



986
1001



987
951



988
1002



989
893



990
975



991
894



992
1009



993
955



994
1004



995
1010



996
957



997
983



998
958



999
987



1000
1012



1001
999



1002
1016



1003
767



1004
989



1005
1003



1006
990



1007
1005



1008
895



1009
1011



1010
1013



1011
959



1012
1006



1013
1014



1014
1017



1015
1018



1016
991



1017
1020



1018
1007



1019
1015



1020
1019



1021
1021



1022
1022



1023
1023










Sequence Q17, having a sequence length of 512:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 65, 20, 256, 34, 24, 36, 7, 129, 66, 11, 40, 68, 130, 19, 13, 48, 14, 72, 257, 21, 132, 35, 258, 22, 80, 136, 25, 37, 260, 264, 26, 96, 38, 67, 41, 144, 28, 69, 42, 272, 49, 70, 160, 44, 131, 73, 288, 192, 50, 74, 52, 15, 133, 320, 81, 23, 134, 384, 76, 56, 259, 82, 137, 27, 97, 39, 84, 138, 145, 261, 29, 43, 98, 88, 140, 30, 146, 71, 262, 265, 161, 45, 100, 51, 148, 46, 75, 266, 273, 104, 162, 53, 193, 152, 77, 164, 268, 274, 54, 83, 57, 112, 135, 78, 289, 194, 85, 276, 58, 168, 139, 99, 86, 60, 280, 89, 290, 196, 141, 101, 147, 176, 142, 321, 90, 200, 31, 292, 322, 263, 149, 102, 105, 296, 304, 163, 92, 47, 267, 150, 208, 385, 386, 324, 106, 153, 165, 55, 328, 113, 154, 79, 269, 108, 224, 166, 195, 270, 275, 291, 169, 59, 114, 277, 156, 87, 197, 116, 170, 61, 281, 278, 177, 293, 388, 91, 198, 172, 120, 201, 336, 62, 282, 143, 103, 178, 294, 93, 202, 323, 392, 297, 107, 180, 151, 209, 284, 94, 204, 298, 400, 352, 325, 155, 210, 305, 300, 109, 184, 115, 167, 225, 326, 306, 157, 329, 110, 117, 212, 171, 330, 226, 387, 308, 216, 416, 271, 279, 158, 337, 118, 332, 389, 173, 121, 199, 179, 228, 338, 390, 122, 448, 312, 393, 283, 174, 394, 181, 340, 203, 353, 63, 295, 285, 232, 124, 286, 205, 182, 299, 354, 211, 401, 185, 396, 344, 240, 206, 95, 327, 402, 356, 307, 301, 417, 213, 186, 404, 227, 418, 302, 111, 360, 331, 214, 309, 188, 449, 217, 408, 229, 159, 420, 310, 333, 119, 368, 339, 391, 313, 218, 334, 230, 233, 175, 123, 450, 341, 220, 314, 424, 395, 355, 287, 183, 234, 125, 342, 452, 397, 432, 316, 345, 241, 207, 403, 357, 187, 236, 126, 242, 398, 346, 456, 358, 405, 303, 189, 215, 361, 244, 348, 419, 406, 464, 362, 409, 219, 311, 421, 369, 190, 248, 231, 410, 364, 335, 480, 315, 221, 422, 370, 425, 235, 451, 412, 343, 222, 317, 372, 426, 453, 237, 433, 347, 243, 454, 318, 376, 428, 238, 359, 457, 399, 434, 349, 458, 245, 363, 127, 407, 436, 465, 246, 350, 460, 249, 411, 365, 440, 466, 371, 423, 366, 250, 413, 468, 481, 191, 373, 427, 414, 252, 374, 482, 429, 455, 223, 472, 377, 435, 484, 319, 430, 239, 378, 459, 437, 488, 380, 461, 496, 351, 467, 438, 247, 462, 441, 442, 469, 251, 367, 253, 375, 444, 470, 483, 415, 485, 473, 474, 254, 379, 431, 489, 486, 476, 439, 490, 463, 381, 497, 492, 443, 382, 498, 445, 471, 500, 446, 475, 487, 504, 477, 255, 491, 478, 383, 493, 499, 494, 501, 502, 447, 505, 506, 479, 508, 495, 503, 507, 509, 510, 511]












Table Q17, having a sequence length of 512:










Reliability or sequence
Polarized channel



number of reliability
sequence number













0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
64



10
9



11
6



12
17



13
10



14
18



15
128



16
12



17
33



18
65



19
20



20
256



21
34



22
24



23
36



24
7



25
129



26
66



27
11



28
40



29
68



30
130



31
19



32
13



33
48



34
14



35
72



36
257



37
21



38
132



39
35



40
258



41
22



42
80



43
136



44
25



45
37



46
260



47
264



48
26



49
96



50
38



51
67



52
41



53
144



54
28



55
69



56
42



57
272



58
49



59
70



60
160



61
44



62
131



63
73



64
288



65
192



66
50



67
74



68
52



69
15



70
133



71
320



72
81



73
23



74
134



75
384



76
76



77
56



78
259



79
82



80
137



81
27



82
97



83
39



84
84



85
138



86
145



87
261



88
29



89
43



90
98



91
88



92
140



93
30



94
146



95
71



96
262



97
265



98
161



99
45



100
100



101
51



102
148



103
46



104
75



105
266



106
273



107
104



108
162



109
53



110
193



111
152



112
77



113
164



114
268



115
274



116
54



117
83



118
57



119
112



120
135



121
78



122
289



123
194



124
85



125
276



126
58



127
168



128
139



129
99



130
86



131
60



132
280



133
89



134
290



135
196



136
141



137
101



138
147



139
176



140
142



141
321



142
90



143
200



144
31



145
292



146
322



147
263



148
149



149
102



150
105



151
296



152
304



153
163



154
92



155
47



156
267



157
150



158
208



159
385



160
386



161
324



162
106



163
153



164
165



165
55



166
328



167
113



168
154



169
79



170
269



171
108



172
224



173
166



174
195



175
270



176
275



177
291



178
169



179
59



180
114



181
277



182
156



183
87



184
197



185
116



186
170



187
61



188
281



189
278



190
177



191
293



192
388



193
91



194
198



195
172



196
120



197
201



198
336



199
62



200
282



201
143



202
103



203
178



204
294



205
93



206
202



207
323



208
392



209
297



210
107



211
180



212
151



213
209



214
284



215
94



216
204



217
298



218
400



219
352



220
325



221
155



222
210



223
305



224
300



225
109



226
184



227
115



228
167



229
225



230
326



231
306



232
157



233
329



234
110



235
117



236
212



237
171



238
330



239
226



240
387



241
308



242
216



243
416



244
271



245
279



246
158



247
337



248
118



249
332



250
389



251
173



252
121



253
199



254
179



255
228



256
338



257
390



258
122



259
448



260
312



261
393



262
283



263
174



264
394



265
181



266
340



267
203



268
353



269
63



270
295



271
285



272
232



273
124



274
286



275
205



276
182



277
299



278
354



279
211



280
401



281
185



282
396



283
344



284
240



285
206



286
95



287
327



288
402



289
356



290
307



291
301



292
417



293
213



294
186



295
404



296
227



297
418



298
302



299
111



300
360



301
331



302
214



303
309



304
188



305
449



306
217



307
408



308
229



309
159



310
420



311
310



312
333



313
119



314
368



315
339



316
391



317
313



318
218



319
334



320
230



321
233



322
175



323
123



324
450



325
341



326
220



327
314



328
424



329
395



330
355



331
287



332
183



333
234



334
125



335
342



336
452



337
397



338
432



339
316



340
345



341
241



342
207



343
403



344
357



345
187



346
236



347
126



348
242



349
398



350
346



351
456



352
358



353
405



354
303



355
189



356
215



357
361



358
244



359
348



360
419



361
406



362
464



363
362



364
409



365
219



366
311



367
421



368
369



369
190



370
248



371
231



372
410



373
364



374
335



375
480



376
315



377
221



378
422



379
370



380
425



381
235



382
451



383
412



384
343



385
222



386
317



387
372



388
426



389
453



390
237



391
433



392
347



393
243



394
454



395
318



396
376



397
428



398
238



399
359



400
457



401
399



402
434



403
349



404
458



405
245



406
363



407
127



408
407



409
436



410
465



411
246



412
350



413
460



414
249



415
411



416
365



417
440



418
466



419
371



420
423



421
366



422
250



423
413



424
468



425
481



426
191



427
373



428
427



429
414



430
252



431
374



432
482



433
429



434
455



435
223



436
472



437
377



438
435



439
484



440
319



441
430



442
239



443
378



444
459



445
437



446
488



447
380



448
461



449
496



450
351



451
467



452
438



453
247



454
462



455
441



456
442



457
469



458
251



459
367



460
253



461
375



462
444



463
470



464
483



465
415



466
485



467
473



468
474



469
254



470
379



471
431



472
489



473
486



474
476



475
439



476
490



477
463



478
381



479
497



480
492



481
443



482
382



483
498



484
445



485
471



486
500



487
446



488
475



489
487



490
504



491
477



492
255



493
491



494
478



495
383



496
493



497
499



498
494



499
501



500
502



501
447



502
505



503
506



504
479



505
508



506
495



507
503



508
507



509
509



510
510



511
511









Sequence Q88, having a sequence length of 256:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 65, 20, 34, 24, 36, 7, 129, 66, 11, 40, 68, 130, 19, 13, 48, 14, 72, 21, 132, 35, 22, 80, 136, 25, 37, 26, 96, 38, 67, 41, 144, 28, 69, 42, 49, 70, 160, 44, 131, 73, 192, 50, 74, 52, 15, 133, 81, 23, 134, 76, 56, 82, 137, 27, 97, 39, 84, 138, 145, 29, 43, 98, 88, 140, 30, 146, 71, 161, 45, 100, 51, 148, 46, 75, 104, 162, 53, 193, 152, 77, 164, 54, 83, 57, 112, 135, 78, 194, 85, 58, 168, 139, 99, 86, 60, 89, 196, 141, 101, 147, 176, 142, 90, 200, 31, 149, 102, 105, 163, 92, 47, 150, 208, 106, 153, 165, 55, 113, 154, 79, 108, 224, 166, 195, 169, 59, 114, 156, 87, 197, 116, 170, 61, 177, 91, 198, 172, 120, 201, 62, 143, 103, 178, 93, 202, 107, 180, 151, 209, 94, 204, 155, 210, 109, 184, 115, 167, 225, 157, 110, 117, 212, 171, 226, 216, 158, 118, 173, 121, 199, 179, 228, 122, 174, 181, 203, 63, 232, 124, 205, 182, 211, 185, 240, 206, 95, 213, 186, 227, 111, 214, 188, 217, 229, 159, 119, 218, 230, 233, 175, 123, 220, 183, 234, 125, 241, 207, 187, 236, 126, 242, 189, 215, 244, 219, 190, 248, 231, 221, 235, 222, 237, 243, 238, 245, 127, 246, 249, 250, 191, 252, 223, 239, 247, 251, 253, 254, 255]









TABLE Q18







having a sequence length of 256:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
64



10
9



11
6



12
17



13
10



14
18



15
128



16
12



17
33



18
65



19
20



20
34



21
24



22
36



23
7



24
129



25
66



26
11



27
40



28
68



29
130



30
19



31
13



32
48



33
14



34
72



35
21



36
132



37
35



38
22



39
80



40
136



41
25



42
37



43
26



44
96



45
38



46
67



47
41



48
144



49
28



50
69



51
42



52
49



53
70



54
160



55
44



56
131



57
73



58
192



59
50



60
74



61
52



62
15



63
133



64
81



65
23



66
134



67
76



68
56



69
82



70
137



71
27



72
97



73
39



74
84



75
138



76
145



77
29



78
43



79
98



80
88



81
140



82
30



83
146



84
71



85
161



86
45



87
100



88
51



89
148



90
46



91
75



92
104



93
162



94
53



95
193



96
152



97
77



98
164



99
54



100
83



101
57



102
112



103
135



104
78



105
194



106
85



107
58



108
168



109
139



110
99



111
86



112
60



113
89



114
196



115
141



116
101



117
147



118
176



119
142



120
90



121
200



122
31



123
149



124
102



125
105



126
163



127
92



128
47



129
150



130
208



131
106



132
153



133
165



134
55



135
113



136
154



137
79



138
108



139
224



140
166



141
195



142
169



143
59



144
114



145
156



146
87



147
197



148
116



149
170



150
61



151
177



152
91



153
198



154
172



155
120



156
201



157
62



158
143



159
103



160
178



161
93



162
202



163
107



164
180



165
151



166
209



167
94



168
204



169
155



170
210



171
109



172
184



173
115



174
167



175
225



176
157



177
110



178
117



179
212



180
171



181
226



182
216



183
158



184
118



185
173



186
121



187
199



188
179



189
228



190
122



191
174



192
181



193
203



194
63



195
232



196
124



197
205



198
182



199
211



200
185



201
240



202
206



203
95



204
213



205
186



206
227



207
111



208
214



209
188



210
217



211
229



212
159



213
119



214
218



215
230



216
233



217
175



218
123



219
220



220
183



221
234



222
125



223
241



224
207



225
187



226
236



227
126



228
242



229
189



230
215



231
244



232
219



233
190



234
248



235
231



236
221



237
235



238
222



239
237



240
243



241
238



242
245



243
127



244
246



245
249



246
250



247
191



248
252



249
223



250
239



251
247



252
251



253
253



254
254



255
255










Sequence Q19, having a sequence length of 128:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 12, 33, 65, 20, 34, 24, 36, 7, 66, 11, 40, 68, 19, 13, 48, 14, 72, 21, 35, 22, 80, 25, 37, 26, 96, 38, 67, 41, 28, 69, 42, 49, 70, 44, 73, 50, 74, 52, 15, 81, 23, 76, 56, 82, 27, 97, 39, 84, 29, 43, 98, 88, 30, 71, 45, 100, 51, 46, 75, 104, 53, 77, 54, 83, 57, 112, 78, 85, 58, 99, 86, 60, 89, 101, 90, 31, 102, 105, 92, 47, 106, 55, 113, 79, 108, 59, 114, 87, 116, 61, 91, 120, 62, 103, 93, 107, 94, 109, 115, 110, 117, 118, 121, 122, 63, 124, 95, 111, 119, 123, 125, 126, 127]












TABLE Q19, having a sequence length of 128:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
64



10
9



11
6



12
17



13
10



14
18



15
12



16
33



17
65



18
20



19
34



20
24



21
36



22
7



23
66



24
11



25
40



26
68



27
19



28
13



29
48



30
14



31
72



32
21



33
35



34
22



35
80



36
25



37
37



38
26



39
96



40
38



41
67



42
41



43
28



44
69



45
42



46
49



47
70



48
44



49
73



50
50



51
74



52
52



53
15



54
81



55
23



56
76



57
56



58
82



59
27



60
97



61
39



62
84



63
29



64
43



65
98



66
88



67
30



68
71



69
45



70
100



71
51



72
46



73
75



74
104



75
53



76
77



77
54



78
83



79
57



80
112



81
78



82
85



83
58



84
99



85
86



86
60



87
89



88
101



89
90



90
31



91
102



92
105



93
92



94
47



95
106



96
55



97
113



98
79



99
108



100
59



101
114



102
87



103
116



104
61



105
91



106
120



107
62



108
103



109
93



110
107



111
94



112
109



113
115



114
110



115
117



116
118



117
121



118
122



119
63



120
124



121
95



122
111



123
119



124
123



125
125



126
126



127
127










Sequence Q20, having a sequence length of 64:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 9, 6, 17, 10, 18, 12, 33, 20, 34, 24, 36, 7, 11, 40, 19, 13, 48, 14, 21, 35, 22, 25, 37, 26, 38, 41, 28, 42, 49, 44, 50, 52, 15, 23, 56, 27, 39, 29, 43, 30, 45, 51, 46, 53, 54, 57, 58, 60, 31, 47, 55, 59, 61, 62, 63]









TABLE Q20







having a sequence length of 64:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
9



10
6



11
17



12
10



13
18



14
12



15
33



16
20



17
34



18
24



19
36



20
7



21
11



22
40



23
19



24
13



25
48



26
14



27
21



28
35



29
22



30
25



31
37



32
26



33
38



34
41



35
28



36
42



37
49



38
44



39
50



40
52



41
15



42
23



43
56



44
27



45
39



46
29



47
43



48
30



49
45



50
51



51
46



52
53



53
54



54
57



55
58



56
60



57
31



58
47



59
55



60
59



61
61



62
62



63
63










Sequence Z16, having a sequence length of 1024:

    • [0, 1, 2, 7, 3, 8, 11, 24, 4, 10, 13, 28, 16, 33, 35, 76, 5, 12, 14, 32, 19, 38, 42, 80, 22, 46, 50, 88, 57, 95, 101, 162, 6, 17, 21, 40, 23, 47, 53, 90, 29, 55, 60, 96, 66, 108, 113, 175, 34, 62, 72, 111, 75, 120, 129, 186, 84, 131, 141, 209, 146, 218, 236, 333, 9, 18, 26, 54, 30, 58, 63, 103, 36, 68, 73, 114, 83, 123, 135, 193, 43, 79, 86, 130, 91, 138, 145, 214, 99, 148, 160, 228, 174, 242, 256, 357, 51, 89, 97, 144, 109, 154, 169, 239, 118, 170, 183, 250, 195, 269, 282, 379, 133, 191, 211, 271, 216, 283, 301, 401, 233, 307, 315, 417, 337, 435, 460, 581, 15, 25, 31, 67, 39, 77, 81, 134, 44, 87, 92, 143, 100, 153, 157, 238, 56, 93, 102, 155, 112, 168, 177, 252, 122, 184, 192, 264, 213, 279, 297, 394, 65, 106, 119, 173, 124, 185, 198, 273, 142, 208, 217, 285, 232, 306, 323, 416, 156, 225, 240, 311, 251, 325, 341, 433, 270, 348, 367, 453, 387, 470, 506, 622, 71, 121, 137, 201, 152, 215, 231, 309, 161, 234, 244, 327, 257, 340, 356, 450, 178, 253, 265, 346, 284, 366, 385, 472, 293, 389, 409, 494, 423, 518, 529, 643, 197, 274, 287, 370, 312, 392, 412, 510, 336, 413, 434, 523, 459, 535, 567, 670, 355, 449, 461, 552, 478, 577, 589, 690, 509, 597, 615, 695, 631, 714, 743, 835, 20, 37, 41, 85, 48, 94, 104, 167, 49, 105, 115, 176, 126, 194, 202, 295, 61, 116, 127, 205, 139, 212, 223, 296, 147, 222, 237, 321, 254, 335, 338, 432, 69, 136, 149, 207, 164, 226, 241, 334, 171, 248, 258, 344, 268, 364, 376, 468, 172, 266, 277, 363, 292, 386, 399, 495, 318, 408, 425, 517, 447, 531, 555, 666, 78, 159, 165, 246, 182, 262, 276, 358, 187, 281, 286, 384, 302, 400, 410, 515, 235, 298, 313, 406, 326, 422, 437, 528, 350, 448, 464, 550, 481, 574, 591, 686, 260, 328, 345, 431, 362, 452, 466, 568, 381, 475, 487, 579, 512, 601, 613, 707, 405, 505, 521, 609, 532, 623, 633, 721, 560, 660, 671, 750, 677, 779, 794, 850, 82, 179, 181, 291, 227, 305, 314, 407, 247, 320, 324, 428, 349, 444, 462, 570, 259, 347, 361, 451, 369, 467, 483, 583, 391, 489, 511, 598, 527, 616, 630, 726, 294, 365, 374, 482, 395, 500, 520, 610, 427, 522, 533, 626, 561, 639, 667, 751, 446, 546, 573, 662, 585, 673, 688, 770, 605, 692, 693, 790, 722, 801, 813, 880, 317, 388, 420, 524, 442, 534, 554, 642, 465, 569, 575, 672, 593, 679, 691, 777, 484, 586, 606, 687, 617, 694, 723, 802, 648, 729, 740, 816, 760, 834, 846, 904, 516, 619, 638, 724, 663, 727, 756, 821, 676, 754, 772, 841, 786, 852, 865, 924, 680, 780, 798, 858, 808, 870, 879, 930, 828, 885, 892, 946, 914, 954, 963, 984, 27, 45, 52, 98, 59, 117, 128, 199, 64, 132, 140, 204, 151, 220, 224, 330, 70, 150, 158, 219, 166, 263, 272, 354, 188, 275, 290, 368, 304, 393, 411, 525, 74, 163, 180, 267, 190, 288, 299, 378, 200, 308, 316, 424, 332, 426, 441, 536, 210, 329, 339, 438, 359, 455, 473, 564, 372, 469, 488, 588, 493, 600, 608, 745, 107, 189, 196, 303, 206, 319, 331, 421, 229, 343, 351, 454, 382, 477, 486, 580, 245, 353, 371, 471, 396, 491, 497, 594, 419, 498, 504, 612, 545, 629, 656, 753, 261, 383, 404, 503, 415, 519, 526, 624, 436, 544, 557, 647, 582, 664, 674, 773, 457, 566, 587, 675, 614, 685, 709, 787, 636, 712, 730, 803, 741, 819, 832, 916, 110, 203, 221, 342, 243, 352, 390, 480, 255, 375, 397, 499, 418, 508, 513, 618, 280, 402, 403, 514, 440, 541, 553, 644, 456, 562, 578, 669, 595, 681, 700, 774, 300, 430, 443, 556, 474, 572, 576, 682, 490, 590, 599, 696, 625, 710, 718, 805, 507, 611, 635, 715, 646, 735, 742, 822, 659, 747, 764, 837, 789, 854, 861, 925, 322, 463, 476, 592, 496, 604, 627, 713, 539, 632, 649, 738, 653, 744, 758, 831, 547, 651, 658, 755, 683, 763, 783, 851, 704, 788, 797, 859, 812, 877, 888, 933, 563, 689, 698, 775, 719, 791, 800, 871, 731, 810, 823, 884, 838, 894, 906, 949, 766, 825, 842, 897, 856, 909, 913, 961, 867, 921, 929, 966, 940, 974, 983, 1003, 125, 230, 249, 373, 278, 398, 414, 530, 289, 429, 439, 543, 458, 559, 584, 701, 310, 445, 479, 571, 492, 596, 603, 706, 501, 607, 628, 728, 650, 736, 749, 829, 360, 485, 502, 602, 538, 621, 637, 739, 542, 641, 655, 746, 665, 759, 769, 849, 548, 661, 678, 768, 703, 782, 795, 860, 716, 807, 811, 876, 824, 889, 900, 944, 377, 537, 540, 645, 549, 652, 668, 762, 565, 684, 697, 778, 711, 792, 809, 874, 634, 702, 720, 796, 732, 817, 826, 886, 761, 827, 844, 898, 857, 908, 915, 960, 654, 734, 748, 818, 767, 839, 848, 902, 785, 853, 864, 912, 873, 922, 932, 969, 799, 869, 878, 928, 891, 935, 943, 976, 903, 947, 953, 981, 958, 989, 991, 1008, 380, 551, 558, 699, 620, 708, 717, 806, 640, 725, 737, 820, 757, 830, 843, 901, 657, 752, 765, 833, 776, 845, 862, 911, 793, 863, 872, 919, 887, 931, 939, 972, 705, 771, 781, 855, 804, 868, 875, 926, 815, 882, 890, 936, 899, 941, 950, 980, 840, 895, 905, 945, 917, 955, 959, 987, 923, 965, 968, 993, 975, 996, 998, 1011, 733, 784, 814, 883, 836, 893, 896, 942, 847, 907, 910, 952, 920, 956, 967, 990, 866, 918, 927, 964, 938, 970, 971, 997, 948, 977, 979, 999, 985, 1004, 1006, 1016, 881, 934, 937, 973, 951, 978, 982, 1001, 957, 986, 988, 1005, 994, 1007, 1012, 1018, 962, 992, 995, 1009, 1000, 1010, 1013, 1019, 1002, 1014, 1015, 1020, 1017, 1021, 1022, 1023]












Table, Z16 having a sequence length of 1024:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
11



7
24



8
4



9
10



10
13



11
28



12
16



13
33



14
35



15
76



16
5



17
12



18
14



19
32



20
19



21
38



22
42



23
80



24
22



25
46



26
50



27
88



28
57



29
95



30
101



31
162



32
6



33
17



34
21



35
40



36
23



37
47



38
53



39
90



40
29



41
55



42
60



43
96



44
66



45
108



46
113



47
175



48
34



49
62



50
72



51
111



52
75



53
120



54
129



55
186



56
84



57
131



58
141



59
209



60
146



61
218



62
236



63
333



64
9



65
18



66
26



67
54



68
30



69
58



70
63



71
103



72
36



73
68



74
73



75
114



76
83



77
123



78
135



79
193



80
43



81
79



82
86



83
130



84
91



85
138



86
145



87
214



88
99



89
148



90
160



91
228



92
174



93
242



94
256



95
357



96
51



97
89



98
97



99
144



100
109



101
154



102
169



103
239



104
118



105
170



106
183



107
250



108
195



109
269



110
282



111
379



112
133



113
191



114
211



115
271



116
216



117
283



118
301



119
401



120
233



121
307



122
315



123
417



124
337



125
435



126
460



127
581



128
15



129
25



130
31



131
67



132
39



133
77



134
81



135
134



136
44



137
87



138
92



139
143



140
100



141
153



142
157



143
238



144
56



145
93



146
102



147
155



148
112



149
168



150
177



151
252



152
122



153
184



154
192



155
264



156
213



157
279



158
297



159
394



160
65



161
106



162
119



163
173



164
124



165
185



166
198



167
273



168
142



169
208



170
217



171
285



172
232



173
306



174
323



175
416



176
156



177
225



178
240



179
311



180
251



181
325



182
341



183
433



184
270



185
348



186
367



187
453



188
387



189
470



190
506



191
622



192
71



193
121



194
137



195
201



196
152



197
215



198
231



199
309



200
161



201
234



202
244



203
327



204
257



205
340



206
356



207
450



208
178



209
253



210
265



211
346



212
284



213
366



214
385



215
472



216
293



217
389



218
409



219
494



220
423



221
518



222
529



223
643



224
197



225
274



226
287



227
370



228
312



229
392



230
412



231
510



232
336



233
413



234
434



235
523



236
459



237
535



238
567



239
670



240
355



241
449



242
461



243
552



244
478



245
577



246
589



247
690



248
509



249
597



250
615



251
695



252
631



253
714



254
743



255
835



256
20



257
37



258
41



259
85



260
48



261
94



262
104



263
167



264
49



265
105



266
115



267
176



268
126



269
194



270
202



271
295



272
61



273
116



274
127



275
205



276
139



277
212



278
223



279
296



280
147



281
222



282
237



283
321



284
254



285
335



286
338



287
432



288
69



289
136



290
149



291
207



292
164



293
226



294
241



295
334



296
171



297
248



298
258



299
344



300
268



301
364



302
376



303
468



304
172



305
266



306
277



307
363



308
292



309
386



310
399



311
495



312
318



313
408



314
425



315
517



316
447



317
531



318
555



319
666



320
78



321
159



322
165



323
246



324
182



325
262



326
276



327
358



328
187



329
281



330
286



331
384



332
302



333
400



334
410



335
515



336
235



337
298



338
313



339
406



340
326



341
422



342
437



343
528



344
350



345
448



346
464



347
550



348
481



349
574



350
591



351
686



352
260



353
328



354
345



355
431



356
362



357
452



358
466



359
568



360
381



361
475



362
487



363
579



364
512



365
601



366
613



367
707



368
405



369
505



370
521



371
609



372
532



373
623



374
633



375
721



376
560



377
660



378
671



379
750



380
677



381
779



382
794



383
850



384
82



385
179



386
181



387
291



388
227



389
305



390
314



391
407



392
247



393
320



394
324



395
428



396
349



397
444



398
462



399
570



400
259



401
347



402
361



403
451



404
369



405
467



406
483



407
583



408
391



409
489



410
511



411
598



412
527



413
616



414
630



415
726



416
294



417
365



418
374



419
482



420
395



421
500



422
520



423
610



424
427



425
522



426
533



427
626



428
561



429
639



430
667



431
751



432
446



433
546



434
573



435
662



436
585



437
673



438
688



439
770



440
605



441
692



442
693



443
790



444
722



445
801



446
813



447
880



448
317



449
388



450
420



451
524



452
442



453
534



454
554



455
642



456
465



457
569



458
575



459
672



460
593



461
679



462
691



463
777



464
484



465
586



466
606



467
687



468
617



469
694



470
723



471
802



472
648



473
729



474
740



475
816



476
760



477
834



478
846



479
904



480
516



481
619



482
638



483
724



484
663



485
727



486
756



487
821



488
676



489
754



490
772



491
841



492
786



493
852



494
865



495
924



496
680



497
780



498
798



499
858



500
808



501
870



502
879



503
930



504
828



505
885



506
892



507
946



508
914



509
954



510
963



511
984



512
27



513
45



514
52



515
98



516
59



517
117



518
128



519
199



520
64



521
132



522
140



523
204



524
151



525
220



526
224



527
330



528
70



529
150



530
158



531
219



532
166



533
263



534
272



535
354



536
188



537
275



538
290



539
368



540
304



541
393



542
411



543
525



544
74



545
163



546
180



547
267



548
190



549
288



550
299



551
378



552
200



553
308



554
316



555
424



556
332



557
426



558
441



559
536



560
210



561
329



562
339



563
438



564
359



565
455



566
473



567
564



568
372



569
469



570
488



571
588



572
493



573
600



574
608



575
745



576
107



577
189



578
196



579
303



580
206



581
319



582
331



583
421



584
229



585
343



586
351



587
454



588
382



589
477



590
486



591
580



592
245



593
353



594
371



595
471



596
396



597
491



598
497



599
594



600
419



601
498



602
504



603
612



604
545



605
629



606
656



607
753



608
261



609
383



610
404



611
503



612
415



613
519



614
526



615
624



616
436



617
544



618
557



619
647



620
582



621
664



622
674



623
773



624
457



625
566



626
587



627
675



628
614



629
685



630
709



631
787



632
636



633
712



634
730



635
803



636
741



637
819



638
832



639
916



640
110



641
203



642
221



643
342



644
243



645
352



646
390



647
480



648
255



649
375



650
397



651
499



652
418



653
508



654
513



655
618



656
280



657
402



658
403



659
514



660
440



661
541



662
553



663
644



664
456



665
562



666
578



667
669



668
595



669
681



670
700



671
774



672
300



673
430



674
443



675
556



676
474



677
572



678
576



679
682



680
490



681
590



682
599



683
696



684
625



685
710



686
718



687
805



688
507



689
611



690
635



691
715



692
646



693
735



694
742



695
822



696
659



697
747



698
764



699
837



700
789



701
854



702
861



703
925



704
322



705
463



706
476



707
592



708
496



709
604



710
627



711
713



712
539



713
632



714
649



715
738



716
653



717
744



718
758



719
831



720
547



721
651



722
658



723
755



724
683



725
763



726
783



727
851



728
704



729
788



730
797



731
859



732
812



733
877



734
888



735
933



736
563



737
689



738
698



739
775



740
719



741
791



742
800



743
871



744
731



745
810



746
823



747
884



748
838



749
894



750
906



751
949



752
766



753
825



754
842



755
897



756
856



757
909



758
913



759
961



760
867



761
921



762
929



763
966



764
940



765
974



766
983



767
1003



768
125



769
230



770
249



771
373



772
278



773
398



774
414



775
530



776
289



777
429



778
439



779
543



780
458



781
559



782
584



783
701



784
310



785
445



786
479



787
571



788
492



789
596



790
603



791
706



792
501



793
607



794
628



795
728



796
650



797
736



798
749



799
829



800
360



801
485



802
502



803
602



804
538



805
621



806
637



807
739



808
542



809
641



810
655



811
746



812
665



813
759



814
769



815
849



816
548



817
661



818
678



819
768



820
703



821
782



822
795



823
860



824
716



825
807



826
811



827
876



828
824



829
889



830
900



831
944



832
377



833
537



834
540



835
645



836
549



837
652



838
668



839
762



840
565



841
684



842
697



843
778



844
711



845
792



846
809



847
874



848
634



849
702



850
720



851
796



852
732



853
817



854
826



855
886



856
761



857
827



858
844



859
898



860
857



861
908



862
915



863
960



864
654



865
734



866
748



867
818



868
767



869
839



870
848



871
902



872
785



873
853



874
864



875
912



876
873



877
922



878
932



879
969



880
799



881
869



882
878



883
928



884
891



885
935



886
943



887
976



888
903



889
947



890
953



891
981



892
958



893
989



894
991



895
1008



896
380



897
551



898
558



899
699



900
620



901
708



902
717



903
806



904
640



905
725



906
737



907
820



908
757



909
830



910
843



911
901



912
657



913
752



914
765



915
833



916
776



917
845



918
862



919
911



920
793



921
863



922
872



923
919



924
887



925
931



926
939



927
972



928
705



929
771



930
781



931
855



932
804



933
868



934
875



935
926



936
815



937
882



938
890



939
936



940
899



941
941



942
950



943
980



944
840



945
895



946
905



947
945



948
917



949
955



950
959



951
987



952
923



953
965



954
968



955
993



956
975



957
996



958
998



959
1011



960
733



961
784



962
814



963
883



964
836



965
893



966
896



967
942



968
847



969
907



970
910



971
952



972
920



973
956



974
967



975
990



976
866



977
918



978
927



979
964



980
938



981
970



982
971



983
997



984
948



985
977



986
979



987
999



988
985



989
1004



990
1006



991
1016



992
881



993
934



994
937



995
973



996
951



997
978



998
982



999
1001



1000
957



1001
986



1002
988



1003
1005



1004
994



1005
1007



1006
1012



1007
1018



1008
962



1009
992



1010
995



1011
1009



1012
1000



1013
1010



1014
1013



1015
1019



1016
1002



1017
1014



1018
1015



1019
1020



1020
1017



1021
1021



1022
1022



1023
1023










Sequence Z17, having a sequence length of 512:

    • [0, 1, 2, 7, 3, 8, 11, 24, 4, 10, 13, 27, 16, 32, 34, 69, 5, 12, 14, 31, 19, 37, 41, 73, 22, 44, 48, 81, 54, 88, 93, 144, 6, 17, 21, 39, 23, 45, 50, 83, 28, 52, 56, 89, 61, 99, 103, 155, 33, 58, 66, 101, 68, 109, 116, 165, 77, 118, 126, 179, 131, 187, 199, 269, 9, 18, 26, 51, 29, 55, 59, 95, 35, 63, 67, 104, 76, 112, 121, 169, 42, 72, 79, 117, 84, 124, 130, 183, 91, 133, 142, 193, 154, 205, 215, 286, 49, 82, 90, 129, 100, 137, 149, 202, 107, 150, 162, 210, 171, 225, 234, 299, 119, 167, 180, 227, 185, 235, 248, 313, 196, 252, 258, 323, 273, 334, 347, 407, 15, 25, 30, 62, 38, 70, 74, 120, 43, 80, 85, 128, 92, 136, 140, 201, 53, 86, 94, 138, 102, 148, 157, 212, 111, 163, 168, 221, 182, 232, 246, 309, 60, 98, 108, 153, 113, 164, 173, 228, 127, 178, 186, 237, 195, 251, 263, 322, 139, 190, 203, 254, 211, 265, 276, 332, 226, 281, 294, 345, 304, 355, 369, 426, 65, 110, 123, 174, 135, 184, 194, 253, 143, 197, 206, 267, 216, 275, 285, 342, 158, 213, 222, 279, 236, 293, 302, 356, 242, 306, 318, 365, 326, 377, 385, 435, 172, 229, 239, 296, 255, 308, 320, 371, 272, 321, 333, 381, 346, 390, 398, 442, 284, 341, 348, 393, 358, 405, 411, 453, 370, 414, 422, 458, 430, 460, 469, 492, 20, 36, 40, 78, 46, 87, 96, 147, 47, 97, 105, 156, 114, 170, 175, 244, 57, 106, 115, 176, 125, 181, 189, 245, 132, 188, 200, 262, 214, 271, 274, 331, 64, 122, 134, 177, 145, 191, 204, 270, 151, 209, 217, 277, 224, 291, 298, 354, 152, 223, 231, 290, 241, 303, 311, 366, 260, 317, 327, 376, 339, 386, 395, 440, 71, 141, 146, 207, 161, 220, 230, 287, 166, 233, 238, 301, 249, 312, 319, 374, 198, 247, 256, 315, 266, 325, 335, 384, 283, 340, 350, 392, 359, 403, 412, 450, 219, 268, 278, 330, 289, 344, 352, 399, 300, 357, 363, 406, 373, 416, 421, 459, 314, 368, 379, 419, 387, 427, 431, 461, 396, 437, 443, 470, 447, 478, 482, 495, 75, 159, 160, 240, 192, 250, 257, 316, 208, 261, 264, 329, 282, 337, 349, 401, 218, 280, 288, 343, 295, 353, 361, 408, 307, 364, 372, 415, 383, 423, 429, 465, 243, 292, 297, 360, 310, 367, 378, 420, 328, 380, 388, 428, 397, 433, 441, 471, 338, 391, 402, 438, 409, 445, 452, 475, 417, 455, 456, 481, 462, 484, 487, 501, 259, 305, 324, 382, 336, 389, 394, 434, 351, 400, 404, 444, 413, 448, 454, 477, 362, 410, 418, 451, 424, 457, 463, 485, 436, 467, 468, 488, 474, 491, 494, 504, 375, 425, 432, 464, 439, 466, 473, 489, 446, 472, 476, 493, 480, 496, 498, 506, 449, 479, 483, 497, 486, 499, 500, 507, 490, 502, 503, 508, 505, 509, 510, 511]












Table Z17, having a sequence length of 512:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
11



7
24



8
4



9
10



10
13



11
27



12
16



13
32



14
34



15
69



16
5



17
12



18
14



19
31



20
19



21
37



22
41



23
73



24
22



25
44



26
48



27
81



28
54



29
88



30
93



31
144



32
6



33
17



34
21



35
39



36
23



37
45



38
50



39
83



40
28



41
52



42
56



43
89



44
61



45
99



46
103



47
155



48
33



49
58



50
66



51
101



52
68



53
109



54
116



55
165



56
77



57
118



58
126



59
179



60
131



61
187



62
199



63
269



64
9



65
18



66
26



67
51



68
29



69
55



70
59



71
95



72
35



73
63



74
67



75
104



76
76



77
112



78
121



79
169



80
42



81
72



82
79



83
117



84
84



85
124



86
130



87
183



88
91



89
133



90
142



91
193



92
154



93
205



94
215



95
286



96
49



97
82



98
90



99
129



100
100



101
137



102
149



103
202



104
107



105
150



106
162



107
210



108
171



109
225



110
234



111
299



112
119



113
167



114
180



115
227



116
185



117
235



118
248



119
313



120
196



121
252



122
258



123
323



124
273



125
334



126
347



127
407



128
15



129
25



130
30



131
62



132
38



133
70



134
74



135
120



136
43



137
80



138
85



139
128



140
92



141
136



142
140



143
201



144
53



145
86



146
94



147
138



148
102



149
148



150
157



151
212



152
111



153
163



154
168



155
221



156
182



157
232



158
246



159
309



160
60



161
98



162
108



163
153



164
113



165
164



166
173



167
228



168
127



169
178



170
186



171
237



172
195



173
251



174
263



175
322



176
139



177
190



178
203



179
254



180
211



181
265



182
276



183
332



184
226



185
281



186
294



187
345



188
304



189
355



190
369



191
426



192
65



193
110



194
123



195
174



196
135



197
184



198
194



199
253



200
143



201
197



202
206



203
267



204
216



205
275



206
285



207
342



208
158



209
213



210
222



211
279



212
236



213
293



214
302



215
356



216
242



217
306



218
318



219
365



220
326



221
377



222
385



223
435



224
172



225
229



226
239



227
296



228
255



229
308



230
320



231
371



232
272



233
321



234
333



235
381



236
346



237
390



238
398



239
442



240
284



241
341



242
348



243
393



244
358



245
405



246
411



247
453



248
370



249
414



250
422



251
458



252
430



253
460



254
469



255
492



256
20



257
36



258
40



259
78



260
46



261
87



262
96



263
147



264
47



265
97



266
105



267
156



268
114



269
170



270
175



271
244



272
57



273
106



274
115



275
176



276
125



277
181



278
189



279
245



280
132



281
188



282
200



283
262



284
214



285
271



286
274



287
331



288
64



289
122



290
134



291
177



292
145



293
191



294
204



295
270



296
151



297
209



298
217



299
277



300
224



301
291



302
298



303
354



304
152



305
223



306
231



307
290



308
241



309
303



310
311



311
366



312
260



313
317



314
327



315
376



316
339



317
386



318
395



319
440



320
71



321
141



322
146



323
207



324
161



325
220



326
230



327
287



328
166



329
233



330
238



331
301



332
249



333
312



334
319



335
374



336
198



337
247



338
256



339
315



340
266



341
325



342
335



343
384



344
283



345
340



346
350



347
392



348
359



349
403



350
412



351
450



352
219



353
268



354
278



355
330



356
289



357
344



358
352



359
399



360
300



361
357



362
363



363
406



364
373



365
416



366
421



367
459



368
314



369
368



370
379



371
419



372
387



373
427



374
431



375
461



376
396



377
437



378
443



379
470



380
447



381
478



382
482



383
495



384
75



385
159



386
160



387
240



388
192



389
250



390
257



391
316



392
208



393
261



394
264



395
329



396
282



397
337



398
349



399
401



400
218



401
280



402
288



403
343



404
295



405
353



406
361



407
408



408
307



409
364



410
372



411
415



412
383



413
423



414
429



415
465



416
243



417
292



418
297



419
360



420
310



421
367



422
378



423
420



424
328



425
380



426
388



427
428



428
397



429
433



430
441



431
471



432
338



433
391



434
402



435
438



436
409



437
445



438
452



439
475



440
417



441
455



442
456



443
481



444
462



445
484



446
487



447
501



448
259



449
305



450
324



451
382



452
336



453
389



454
394



455
434



456
351



457
400



458
404



459
444



460
413



461
448



462
454



463
477



464
362



465
410



466
418



467
451



468
424



469
457



470
463



471
485



472
436



473
467



474
468



475
488



476
474



477
491



478
494



479
504



480
375



481
425



482
432



483
464



484
439



485
466



486
473



487
489



488
446



489
472



490
476



491
493



492
480



493
496



494
498



495
506



496
449



497
479



498
483



499
497



500
486



501
499



502
500



503
507



504
490



505
502



506
503



507
508



508
505



509
509



510
510



511
511










Sequence Z18, having a sequence length of 256:

    • [0, 1, 2, 7, 3, 8, 11, 23, 4, 10, 13, 26, 16, 31, 33, 62, 5, 12, 14, 30, 19, 35, 38, 65, 21, 41, 43, 71, 49, 77, 82, 122, 6, 17, 20, 37, 22, 42, 45, 73, 27, 47, 51, 78, 55, 86, 90, 128, 32, 52, 59, 88, 61, 94, 99, 134, 68, 101, 107, 143, 112, 150, 157, 194, 9, 18, 25, 46, 28, 50, 53, 84, 34, 57, 60, 91, 67, 97, 104, 137, 39, 64, 69, 100, 74, 106, 111, 146, 80, 113, 120, 152, 127, 161, 167, 203, 44, 72, 79, 110, 87, 116, 124, 159, 92, 125, 131, 163, 138, 171, 177, 207, 102, 135, 144, 173, 148, 178, 184, 213, 155, 186, 190, 218, 196, 222, 227, 243, 15, 24, 29, 56, 36, 63, 66, 103, 40, 70, 75, 109, 81, 115, 119, 158, 48, 76, 83, 117, 89, 123, 129, 165, 96, 132, 136, 169, 145, 176, 183, 212, 54, 85, 93, 126, 98, 133, 140, 174, 108, 142, 149, 180, 154, 185, 191, 217, 118, 151, 160, 188, 164, 192, 198, 220, 172, 200, 205, 225, 209, 229, 233, 247, 58, 95, 105, 141, 114, 147, 153, 187, 121, 156, 162, 193, 168, 197, 202, 224, 130, 166, 170, 199, 179, 204, 208, 230, 182, 210, 214, 232, 219, 236, 238, 249, 139, 175, 181, 206, 189, 211, 215, 235, 195, 216, 221, 237, 226, 239, 241, 250, 201, 223, 228, 240, 231, 242, 244, 251, 234, 245, 246, 252, 248, 253, 254, 255]












TABLE Z18, having a sequence length of 256:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
11



7
23



8
4



9
10



10
13



11
26



12
16



13
31



14
33



15
62



16
5



17
12



18
14



19
30



20
19



21
35



22
38



23
65



24
21



25
41



26
43



27
71



28
49



29
77



30
82



31
122



32
6



33
17



34
20



35
37



36
22



37
42



38
45



39
73



40
27



41
47



42
51



43
78



44
55



45
86



46
90



47
128



48
32



49
52



50
59



51
88



52
61



53
94



54
99



55
134



56
68



57
101



58
107



59
143



60
112



61
150



62
157



63
194



64
9



65
18



66
25



67
46



68
28



69
50



70
53



71
84



72
34



73
57



74
60



75
91



76
67



77
97



78
104



79
137



80
39



81
64



82
69



83
100



84
74



85
106



86
111



87
146



88
80



89
113



90
120



91
152



92
127



93
161



94
167



95
203



96
44



97
72



98
79



99
110



100
87



101
116



102
124



103
159



104
92



105
125



106
131



107
163



108
138



109
171



110
177



111
207



112
102



113
135



114
144



115
173



116
148



117
178



118
184



119
213



120
155



121
186



122
190



123
218



124
196



125
222



126
227



127
243



128
15



129
24



130
29



131
56



132
36



133
63



134
66



135
103



136
40



137
70



138
75



139
109



140
81



141
115



142
119



143
158



144
48



145
76



146
83



147
117



148
89



149
123



150
129



151
165



152
96



153
132



154
136



155
169



156
145



157
176



158
183



159
212



160
54



161
85



162
93



163
126



164
98



165
133



166
140



167
174



168
108



169
142



170
149



171
180



172
154



173
185



174
191



175
217



176
118



177
151



178
160



179
188



180
164



181
192



182
198



183
220



184
172



185
200



186
205



187
225



188
209



189
229



190
233



191
247



192
58



193
95



194
105



195
141



196
114



197
147



198
153



199
187



200
121



201
156



202
162



203
193



204
168



205
197



206
202



207
224



208
130



209
166



210
170



211
199



212
179



213
204



214
208



215
230



216
182



217
210



218
214



219
232



220
219



221
236



222
238



223
249



224
139



225
175



226
181



227
206



228
189



229
211



230
215



231
235



232
195



233
216



234
221



235
237



236
226



237
239



238
241



239
250



240
201



241
223



242
228



243
240



244
231



245
242



246
244



247
251



248
234



249
245



250
246



251
252



252
248



253
253



254
254



255
255










Sequence Z19, having a sequence length of 128:

    • [0, 1, 2, 7, 3, 8, 11, 22, 4, 10, 13, 24, 15, 28, 30, 53, 5, 12, 14, 27, 18, 32, 34, 55, 20, 36, 38, 59, 43, 63, 67, 90, 6, 16, 19, 33, 21, 37, 40, 61, 25, 42, 45, 64, 48, 69, 72, 94, 29, 46, 50, 71, 52, 75, 77, 96, 57, 79, 83, 100, 86, 104, 107, 119, 9, 17, 23, 41, 26, 44, 47, 68, 31, 49, 51, 73, 56, 76, 81, 98, 35, 54, 58, 78, 62, 82, 85, 102, 66, 87, 89, 105, 93, 109, 111, 121, 39, 60, 65, 84, 70, 88, 91, 108, 74, 92, 95, 110, 99, 112, 114, 122, 80, 97, 101, 113, 103, 115, 116, 123, 106, 117, 118, 124, 120, 125, 126, 127]












Table Z19, having a sequence length of 128:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
11



7
22



8
4



9
10



10
13



11
24



12
15



13
28



14
30



15
53



16
5



17
12



18
14



19
27



20
18



21
32



22
34



23
55



24
20



25
36



26
38



27
59



28
43



29
63



30
67



31
90



32
6



33
16



34
19



35
33



36
21



37
37



38
40



39
61



40
25



41
42



42
45



43
64



44
48



45
69



46
72



47
94



48
29



49
46



50
50



51
71



52
52



53
75



54
77



55
96



56
57



57
79



58
83



59
100



60
86



61
104



62
107



63
119



64
9



65
17



66
23



67
41



68
26



69
44



70
47



71
68



72
31



73
49



74
51



75
73



76
56



77
76



78
81



79
98



80
35



81
54



82
58



83
78



84
62



85
82



86
85



87
102



88
66



89
87



90
89



91
105



92
93



93
109



94
111



95
121



96
39



97
60



98
65



99
84



100
70



101
88



102
91



103
108



104
74



105
92



106
95



107
110



108
99



109
112



110
114



111
122



112
80



113
97



114
101



115
113



116
103



117
115



118
116



119
123



120
106



121
117



122
118



123
124



124
120



125
125



126
126



127
127










Sequence Z20, having a sequence length of 64:

    • [0, 1, 2, 7, 3, 8, 10, 20, 4, 9, 12, 21, 14, 24, 26, 41, 5, 11, 13, 23, 16, 27, 29, 42, 18, 30, 32, 44, 35, 46, 48, 57, 6, 15, 17, 28, 19, 31, 33, 45, 22, 34, 36, 47, 38, 49, 51, 58, 25, 37, 39, 50, 40, 52, 53, 59, 43, 54, 55, 60, 56, 61, 62, 63]












TABLE Z20, having a sequence length of 64:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
10



7
20



8
4



9
9



10
12



11
21



12
14



13
24



14
26



15
41



16
5



17
11



18
13



19
23



20
16



21
27



22
29



23
42



24
18



25
30



26
32



27
44



28
35



29
46



30
48



31
57



32
6



33
15



34
17



35
28



36
19



37
31



38
33



39
45



40
22



41
34



42
36



43
47



44
38



45
49



46
51



47
58



48
25



49
37



50
39



51
50



52
40



53
52



54
53



55
59



56
43



57
54



58
55



59
60



60
56



61
61



62
62



63
63










Fifth group of sequences (a criterion that preferentially considers a minimum code distance).


Sequence Q21, having a sequence length of 1024:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 6, 9, 17, 10, 18, 128, 12, 33, 256, 20, 34, 24, 65, 36, 7, 129, 66, 512, 11, 40, 68, 19, 13, 130, 48, 14, 72, 257, 21, 132, 35, 258, 26, 513, 80, 37, 25, 22, 136, 96, 260, 38, 514, 264, 67, 41, 144, 28, 69, 42, 516, 49, 160, 272, 70, 520, 288, 528, 131, 44, 544, 73, 192, 50, 74, 52, 15, 133, 320, 81, 23, 134, 76, 137, 82, 384, 56, 27, 97, 39, 259, 84, 138, 145, 261, 29, 43, 98, 515, 88, 140, 30, 146, 71, 262, 265, 517, 161, 45, 576, 518, 100, 51, 148, 521, 46, 75, 640, 266, 273, 522, 104, 162, 53, 193, 152, 77, 164, 268, 274, 54, 83, 530, 57, 112, 529, 524, 135, 78, 289, 194, 85, 276, 58, 168, 139, 99, 86, 60, 89, 768, 196, 290, 141, 101, 280, 545, 546, 532, 147, 176, 142, 90, 536, 292, 200, 263, 31, 149, 321, 322, 577, 102, 105, 296, 163, 92, 47, 150, 548, 208, 324, 385, 304, 267, 578, 106, 153, 386, 165, 55, 328, 113, 519, 552, 641, 154, 79, 108, 224, 269, 166, 523, 560, 580, 195, 277, 169, 275, 291, 59, 270, 114, 156, 87, 197, 116, 170, 61, 525, 531, 177, 278, 281, 526, 642, 293, 388, 91, 584, 769, 198, 172, 120, 201, 62, 143, 336, 282, 103, 178, 294, 93, 533, 644, 534, 547, 770, 392, 297, 592, 323, 202, 284, 151, 209, 180, 107, 325, 94, 537, 400, 298, 204, 352, 305, 155, 300, 210, 608, 648, 109, 184, 115, 167, 225, 326, 157, 110, 772, 549, 656, 538, 117, 212, 330, 171, 550, 329, 306, 226, 387, 308, 271, 579, 416, 216, 337, 158, 776, 118, 540, 553, 279, 332, 389, 173, 121, 199, 179, 228, 283, 122, 393, 174, 312, 672, 390, 554, 556, 203, 561, 181, 295, 448, 353, 338, 63, 581, 340, 285, 394, 232, 124, 354, 582, 784, 704, 527, 286, 182, 562, 643, 585, 205, 299, 211, 401, 185, 396, 240, 586, 645, 593, 535, 301, 402, 344, 206, 564, 800, 327, 356, 307, 95, 417, 213, 186, 404, 111, 539, 568, 594, 649, 771, 302, 832, 588, 646, 227, 360, 214, 188, 551, 609, 896, 331, 309, 418, 449, 217, 408, 229, 541, 159, 420, 596, 650, 773, 310, 333, 119, 368, 339, 391, 657, 313, 218, 542, 610, 334, 230, 233, 774, 658, 612, 175, 123, 450, 652, 341, 220, 557, 314, 555, 600, 583, 424, 395, 777, 673, 355, 287, 183, 234, 125, 342, 563, 674, 616, 558, 660, 778, 452, 397, 432, 316, 345, 241, 207, 785, 403, 357, 187, 587, 565, 664, 624, 780, 236, 126, 242, 398, 705, 346, 456, 358, 405, 303, 569, 595, 189, 786, 215, 676, 589, 566, 647, 361, 706, 244, 348, 419, 406, 311, 708, 219, 598, 601, 651, 611, 409, 680, 788, 362, 570, 597, 572, 464, 801, 590, 421, 802, 369, 792, 190, 602, 653, 248, 688, 231, 410, 364, 335, 422, 613, 659, 654, 315, 221, 370, 425, 235, 451, 480, 775, 412, 614, 343, 222, 317, 372, 543, 426, 453, 237, 559, 833, 804, 712, 834, 661, 808, 779, 617, 604, 433, 720, 816, 836, 347, 897, 243, 662, 454, 318, 675, 376, 428, 625, 238, 359, 567, 618, 665, 736, 898, 457, 399, 781, 591, 666, 678, 349, 434, 677, 840, 782, 626, 571, 620, 787, 363, 245, 458, 127, 407, 436, 465, 350, 246, 681, 460, 249, 599, 411, 365, 668, 707, 573, 789, 803, 790, 682, 440, 709, 466, 628, 371, 423, 366, 250, 413, 574, 468, 603, 481, 689, 793, 191, 373, 655, 900, 805, 427, 615, 710, 414, 252, 848, 684, 713, 605, 690, 632, 482, 794, 806, 472, 223, 663, 835, 904, 809, 714, 619, 796, 374, 429, 455, 692, 721, 837, 716, 864, 810, 606, 912, 722, 696, 377, 817, 435, 812, 484, 319, 430, 621, 838, 667, 239, 378, 459, 437, 627, 622, 488, 380, 461, 679, 841, 818, 724, 669, 496, 629, 928, 737, 899, 783, 738, 901, 842, 438, 467, 247, 820, 849, 683, 351, 791, 441, 728, 670, 462, 469, 442, 251, 367, 630, 740, 902, 711, 844, 850, 905, 685, 691, 824, 633, 483, 795, 744, 470, 852, 686, 444, 473, 253, 634, 485, 415, 375, 960, 865, 575, 807, 906, 715, 913, 693, 797, 866, 811, 717, 474, 254, 694, 723, 636, 486, 798, 607, 697, 489, 431, 379, 908, 752, 914, 856, 868, 839, 929, 813, 718, 819, 476, 916, 725, 698, 490, 739, 814, 843, 623, 497, 439, 381, 671, 463, 726, 930, 872, 821, 920, 700, 729, 492, 932, 961, 741, 903, 845, 498, 880, 382, 822, 851, 631, 443, 825, 730, 471, 445, 687, 635, 742, 846, 500, 745, 826, 732, 446, 962, 936, 255, 853, 504, 637, 907, 475, 746, 867, 487, 695, 799, 854, 828, 753, 857, 964, 909, 719, 477, 915, 869, 699, 748, 944, 638, 754, 491, 910, 858, 478, 815, 727, 917, 870, 493, 873, 701, 968, 383, 860, 756, 918, 931, 976, 499, 921, 874, 702, 823, 494, 731, 760, 881, 933, 501, 743, 922, 876, 847, 934, 827, 733, 502, 992, 882, 447, 963, 937, 747, 505, 855, 924, 734, 829, 884, 938, 506, 965, 749, 945, 966, 940, 969, 911, 946, 755, 888, 830, 859, 639, 871, 970, 750, 508, 948, 977, 757, 479, 919, 861, 875, 972, 978, 758, 862, 952, 761, 993, 923, 703, 495, 935, 877, 883, 980, 762, 925, 994, 878, 503, 885, 939, 984, 764, 996, 926, 735, 967, 886, 941, 507, 947, 889, 831, 1000, 942, 971, 751, 509, 949, 890, 973, 1008, 510, 950, 979, 759, 892, 863, 953, 974, 981, 954, 763, 995, 879, 982, 956, 985, 765, 997, 927, 887, 986, 766, 998, 1001, 943, 891, 988, 1002, 1009, 511, 951, 893, 1004, 975, 1010, 894, 955, 1012, 983, 957, 1016, 958, 987, 767, 999, 989, 1003, 990, 1005, 1011, 895, 1006, 1013, 1014, 1017, 959, 1018, 1020, 991, 1007, 1015, 1019, 1021, 1022, 1023]












Table Q21, having a sequence length of 1024:










Reliability or




sequence number
Polarized channel



of reliability
sequence number














0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
64



10
6



11
9



12
17



13
10



14
18



15
128



16
12



17
33



18
256



19
20



20
34



21
24



22
65



23
36



24
7



25
129



26
66



27
512



28
11



29
40



30
68



31
19



32
13



33
130



34
48



35
14



36
72



37
257



38
21



39
132



40
35



41
258



42
26



43
513



44
80



45
37



46
25



47
22



48
136



49
96



50
260



51
38



52
514



53
264



54
67



55
41



56
144



57
28



58
69



59
42



60
516



61
49



62
160



63
272



64
70



65
520



66
288



67
528



68
131



69
44



70
544



71
73



72
192



73
50



74
74



75
52



76
15



77
133



78
320



79
81



80
23



81
134



82
76



83
137



84
82



85
384



86
56



87
27



88
97



89
39



90
259



91
84



92
138



93
145



94
261



95
29



96
43



97
98



98
515



99
88



100
140



101
30



102
146



103
71



104
262



105
265



106
517



107
161



108
45



109
576



110
518



111
100



112
51



113
148



114
521



115
46



116
75



117
640



118
266



119
273



120
522



121
104



122
162



123
53



124
193



125
152



126
77



127
164



128
268



129
274



130
54



131
83



132
530



133
57



134
112



135
529



136
524



137
135



138
78



139
289



140
194



141
85



142
276



143
58



144
168



145
139



146
99



147
86



148
60



149
89



150
768



151
196



152
290



153
141



154
101



155
280



156
545



157
546



158
532



159
147



160
176



161
142



162
90



163
536



164
292



165
200



166
263



167
31



168
149



169
321



170
322



171
577



172
102



173
105



174
296



175
163



176
92



177
47



178
150



179
548



180
208



181
324



182
385



183
304



184
267



185
578



186
106



187
153



188
386



189
165



190
55



191
328



192
113



193
519



194
552



195
641



196
154



197
79



198
108



199
224



200
269



201
166



202
523



203
560



204
580



205
195



206
277



207
169



208
275



209
291



210
59



211
270



212
114



213
156



214
87



215
197



216
116



217
170



218
61



219
525



220
531



221
177



222
278



223
281



224
526



225
642



226
293



227
388



228
91



229
584



230
769



231
198



232
172



233
120



234
201



235
62



236
143



237
336



238
282



239
103



240
178



241
294



242
93



243
533



244
644



245
534



246
547



247
770



248
392



249
297



250
592



251
323



252
202



253
284



254
151



255
209



256
180



257
107



258
325



259
94



260
537



261
400



262
298



263
204



264
352



265
305



266
155



267
300



268
210



269
608



270
648



271
109



272
184



273
115



274
167



275
225



276
326



277
157



278
110



279
772



280
549



281
656



282
538



283
117



284
212



285
330



286
171



287
550



288
329



289
306



290
226



291
387



292
308



293
271



294
579



295
416



296
216



297
337



298
158



299
776



300
118



301
540



302
553



303
279



304
332



305
389



306
173



307
121



308
199



309
179



310
228



311
283



312
122



313
393



314
174



315
312



316
672



317
390



318
554



319
556



320
203



321
561



322
181



323
295



324
448



325
353



326
338



327
63



328
581



329
340



330
285



331
394



332
232



333
124



334
354



335
582



336
784



337
704



338
527



339
286



340
182



341
562



342
643



343
585



344
205



345
299



346
211



347
401



348
185



349
396



350
240



351
586



352
645



353
593



354
535



355
301



356
402



357
344



358
206



359
564



360
800



361
327



362
356



363
307



364
95



365
417



366
213



367
186



368
404



369
111



370
539



371
568



372
594



373
649



374
771



375
302



376
832



377
588



378
646



379
227



380
360



381
214



382
188



383
551



384
609



385
896



386
331



387
309



388
418



389
449



390
217



391
408



392
229



393
541



394
159



395
420



396
596



397
650



398
773



399
310



400
333



401
119



402
368



403
339



404
391



405
657



406
313



407
218



408
542



409
610



410
334



411
230



412
233



413
774



414
658



415
612



416
175



417
123



418
450



419
652



420
341



421
220



422
557



423
314



424
555



425
600



426
583



427
424



428
395



429
777



430
673



431
355



432
287



433
183



434
234



435
125



436
342



437
563



438
674



439
616



440
558



441
660



442
778



443
452



444
397



445
432



446
316



447
345



448
241



449
207



450
785



451
403



452
357



453
187



454
587



455
565



456
664



457
624



458
780



459
236



460
126



461
242



462
398



463
705



464
346



465
456



466
358



467
405



468
303



469
569



470
595



471
189



472
786



473
215



474
676



475
589



476
566



477
647



478
361



479
706



480
244



481
348



482
419



483
406



484
311



485
708



486
219



487
598



488
601



489
651



490
611



491
409



492
680



493
788



494
362



495
570



496
597



497
572



498
464



499
801



500
590



501
421



502
802



503
369



504
792



505
190



506
602



507
653



508
248



509
688



510
231



511
410



512
364



513
335



514
422



515
613



516
659



517
654



518
315



519
221



520
370



521
425



522
235



523
451



524
480



525
775



526
412



527
614



528
343



529
222



530
317



531
372



532
543



533
426



534
453



535
237



536
559



537
833



538
804



539
712



540
834



541
661



542
808



543
779



544
617



545
604



546
433



547
720



548
816



549
836



550
347



551
897



552
243



553
662



554
454



555
318



556
675



557
376



558
428



559
625



560
238



561
359



562
567



563
618



564
665



565
736



566
898



567
457



568
399



569
781



570
591



571
666



572
678



573
349



574
434



575
677



576
840



577
782



578
626



579
571



580
620



581
787



582
363



583
245



584
458



585
127



586
407



587
436



588
465



589
350



590
246



591
681



592
460



593
249



594
599



595
411



596
365



597
668



598
707



599
573



600
789



601
803



602
790



603
682



604
440



605
709



606
466



607
628



608
371



609
423



610
366



611
250



612
413



613
574



614
468



615
603



616
481



617
689



618
793



619
191



620
373



621
655



622
900



623
805



624
427



625
615



626
710



627
414



628
252



629
848



630
684



631
713



632
605



633
690



634
632



635
482



636
794



637
806



638
472



639
223



640
663



641
835



642
904



643
809



644
714



645
619



646
796



647
374



648
429



649
455



650
692



651
721



652
837



653
716



654
864



655
810



656
606



657
912



658
722



659
696



660
377



661
817



662
435



663
812



664
484



665
319



666
430



667
621



668
838



669
667



670
239



671
378



672
459



673
437



674
627



675
622



676
488



677
380



678
461



679
679



680
841



681
818



682
724



683
669



684
496



685
629



686
928



687
737



688
899



689
783



690
738



691
901



692
842



693
438



694
467



695
247



696
820



697
849



698
683



699
351



700
791



701
441



702
728



703
670



704
462



705
469



706
442



707
251



708
367



709
630



710
740



711
902



712
711



713
844



714
850



715
905



716
685



717
691



718
824



719
633



720
483



721
795



722
744



723
470



724
852



725
686



726
444



727
473



728
253



729
634



730
485



731
415



732
375



733
960



734
865



735
575



736
807



737
906



738
715



739
913



740
693



741
797



742
866



743
811



744
717



745
474



746
254



747
694



748
723



749
636



750
486



751
798



752
607



753
697



754
489



755
431



756
379



757
908



758
752



759
914



760
856



761
868



762
839



763
929



764
813



765
718



766
819



767
476



768
916



769
725



770
698



771
490



772
739



773
814



774
843



775
623



776
497



777
439



778
381



779
671



780
463



781
726



782
930



783
872



784
821



785
920



786
700



787
729



788
492



789
932



790
961



791
741



792
903



793
845



794
498



795
880



796
382



797
822



798
851



799
631



800
443



801
825



802
730



803
471



804
445



805
687



806
635



807
742



808
846



809
500



810
745



811
826



812
732



813
446



814
962



815
936



816
255



817
853



818
504



819
637



820
907



821
475



822
746



823
867



824
487



825
695



826
799



827
854



828
828



829
753



830
857



831
964



832
909



833
719



834
477



835
915



836
869



837
699



838
748



839
944



840
638



841
754



842
491



843
910



844
858



845
478



846
815



847
727



848
917



849
870



850
493



851
873



852
701



853
968



854
383



855
860



856
756



857
918



858
931



859
976



860
499



861
921



862
874



863
702



864
823



865
494



866
731



867
760



868
881



869
933



870
501



871
743



872
922



873
876



874
847



875
934



876
827



877
733



878
502



879
992



880
882



881
447



882
963



883
937



884
747



885
505



886
855



887
924



888
734



889
829



890
884



891
938



892
506



893
965



894
749



895
945



896
966



897
940



898
969



899
911



900
946



901
755



902
888



903
830



904
859



905
639



906
871



907
970



908
750



909
508



910
948



911
977



912
757



913
479



914
919



915
861



916
875



917
972



918
978



919
758



920
862



921
952



922
761



923
993



924
923



925
703



926
495



927
935



928
877



929
883



930
980



931
762



932
925



933
994



934
878



935
503



936
885



937
939



938
984



939
764



940
996



941
926



942
735



943
967



944
886



945
941



946
507



947
947



948
889



949
831



950
1000



951
942



952
971



953
751



954
509



955
949



956
890



957
973



958
1008



959
510



960
950



961
979



962
759



963
892



964
863



965
953



966
974



967
981



968
954



969
763



970
995



971
879



972
982



973
956



974
985



975
765



976
997



977
927



978
887



979
986



980
766



981
998



982
1001



983
943



984
891



985
988



986
1002



987
1009



988
511



989
951



990
893



991
1004



992
975



993
1010



994
894



995
955



996
1012



997
983



998
957



999
1016



1000
958



1001
987



1002
767



1003
999



1004
989



1005
1003



1006
990



1007
1005



1008
1011



1009
895



1010
1006



1011
1013



1012
1014



1013
1017



1014
959



1015
1018



1016
1020



1017
991



1018
1007



1019
1015



1020
1019



1021
1021



1022
1022



1023
1023










Sequence Q22, having a sequence length of 512:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 6, 9, 17, 10, 18, 128, 12, 33, 256, 20, 34, 24, 65, 36, 7, 129, 66, 11, 40, 68, 19, 13, 130, 48, 14, 72, 257, 21, 132, 35, 258, 26, 80, 37, 25, 22, 136, 96, 260, 38, 264, 67, 41, 144, 28, 69, 42, 49, 160, 272, 70, 288, 131, 44, 73, 192, 50, 74, 52, 15, 133, 320, 81, 23, 134, 76, 137, 82, 384, 56, 27, 97, 39, 259, 84, 138, 145, 261, 29, 43, 98, 88, 140, 30, 146, 71, 262, 265, 161, 45, 100, 51, 148, 46, 75, 266, 273, 104, 162, 53, 193, 152, 77, 164, 268, 274, 54, 83, 57, 112, 135, 78, 289, 194, 85, 276, 58, 168, 139, 99, 86, 60, 89, 196, 290, 141, 101, 280, 147, 176, 142, 90, 292, 200, 263, 31, 149, 321, 322, 102, 105, 296, 163, 92, 47, 150, 208, 324, 385, 304, 267, 106, 153, 386, 165, 55, 328, 113, 154, 79, 108, 224, 269, 166, 195, 277, 169, 275, 291, 59, 270, 114, 156, 87, 197, 116, 170, 61, 177, 278, 281, 293, 388, 91, 198, 172, 120, 201, 62, 143, 336, 282, 103, 178, 294, 93, 392, 297, 323, 202, 284, 151, 209, 180, 107, 325, 94, 400, 298, 204, 352, 305, 155, 300, 210, 109, 184, 115, 167, 225, 326, 157, 110, 117, 212, 330, 171, 329, 306, 226, 387, 308, 271, 416, 216, 337, 158, 118, 279, 332, 389, 173, 121, 199, 179, 228, 283, 122, 393, 174, 312, 390, 203, 181, 295, 448, 353, 338, 63, 340, 285, 394, 232, 124, 354, 286, 182, 205, 299, 211, 401, 185, 396, 240, 301, 402, 344, 206, 327, 356, 307, 95, 417, 213, 186, 404, 111, 302, 227, 360, 214, 188, 331, 309, 418, 449, 217, 408, 229, 159, 420, 310, 333, 119, 368, 339, 391, 313, 218, 334, 230, 233, 175, 123, 450, 341, 220, 314, 424, 395, 355, 287, 183, 234, 125, 342, 452, 397, 432, 316, 345, 241, 207, 403, 357, 187, 236, 126, 242, 398, 346, 456, 358, 405, 303, 189, 215, 361, 244, 348, 419, 406, 311, 219, 409, 362, 464, 421, 369, 190, 248, 231, 410, 364, 335, 422, 315, 221, 370, 425, 235, 451, 480, 412, 343, 222, 317, 372, 426, 453, 237, 433, 347, 243, 454, 318, 376, 428, 238, 359, 457, 399, 349, 434, 363, 245, 458, 127, 407, 436, 465, 350, 246, 460, 249, 411, 365, 440, 466, 371, 423, 366, 250, 413, 468, 481, 191, 373, 427, 414, 252, 482, 472, 223, 374, 429, 455, 377, 435, 484, 319, 430, 239, 378, 459, 437, 488, 380, 461, 496, 438, 467, 247, 351, 441, 462, 469, 442, 251, 367, 483, 470, 444, 473, 253, 485, 415, 375, 474, 254, 486, 489, 431, 379, 476, 490, 497, 439, 381, 463, 492, 498, 382, 443, 471, 445, 500, 446, 255, 504, 475, 487, 477, 491, 478, 493, 383, 499, 494, 501, 502, 447, 505, 506, 508, 479, 495, 503, 507, 509, 510, 511]












TABLE Q22, having a sequence length of 512:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
64



10
6



11
9



12
17



13
10



14
18



15
128



16
12



17
33



18
256



19
20



20
34



21
24



22
65



23
36



24
7



25
129



26
66



27
11



28
40



29
68



30
19



31
13



32
130



33
48



34
14



35
72



36
257



37
21



38
132



39
35



40
258



41
26



42
80



43
37



44
25



45
22



46
136



47
96



48
260



49
38



50
264



51
67



52
41



53
144



54
28



55
69



56
42



57
49



58
160



59
272



60
70



61
288



62
131



63
44



64
73



65
192



66
50



67
74



68
52



69
15



70
133



71
320



72
81



73
23



74
134



75
76



76
137



77
82



78
384



79
56



80
27



81
97



82
39



83
259



84
84



85
138



86
145



87
261



88
29



89
43



90
98



91
88



92
140



93
30



94
146



95
71



96
262



97
265



98
161



99
45



100
100



101
51



102
148



103
46



104
75



105
266



106
273



107
104



108
162



109
53



110
193



111
152



112
77



113
164



114
268



115
274



116
54



117
83



118
57



119
112



120
135



121
78



122
289



123
194



124
85



125
276



126
58



127
168



128
139



129
99



130
86



131
60



132
89



133
196



134
290



135
141



136
101



137
280



138
147



139
176



140
142



141
90



142
292



143
200



144
263



145
31



146
149



147
321



148
322



149
102



150
105



151
296



152
163



153
92



154
47



155
150



156
208



157
324



158
385



159
304



160
267



161
106



162
153



163
386



164
165



165
55



166
328



167
113



168
154



169
79



170
108



171
224



172
269



173
166



174
195



175
277



176
169



177
275



178
291



179
59



180
270



181
114



182
156



183
87



184
197



185
116



186
170



187
61



188
177



189
278



190
281



191
293



192
388



193
91



194
198



195
172



196
120



197
201



198
62



199
143



200
336



201
282



202
103



203
178



204
294



205
93



206
392



207
297



208
323



209
202



210
284



211
151



212
209



213
180



214
107



215
325



216
94



217
400



218
298



219
204



220
352



221
305



222
155



223
300



224
210



225
109



226
184



227
115



228
167



229
225



230
326



231
157



232
110



233
117



234
212



235
330



236
171



237
329



238
306



239
226



240
387



241
308



242
271



243
416



244
216



245
337



246
158



247
118



248
279



249
332



250
389



251
173



252
121



253
199



254
179



255
228



256
283



257
122



258
393



259
174



260
312



261
390



262
203



263
181



264
295



265
448



266
353



267
338



268
63



269
340



270
285



271
394



272
232



273
124



274
354



275
286



276
182



277
205



278
299



279
211



280
401



281
185



282
396



283
240



284
301



285
402



286
344



287
206



288
327



289
356



290
307



291
95



292
417



293
213



294
186



295
404



296
111



297
302



298
227



299
360



300
214



301
188



302
331



303
309



304
418



305
449



306
217



307
408



308
229



309
159



310
420



311
310



312
333



313
119



314
368



315
339



316
391



317
313



318
218



319
334



320
230



321
233



322
175



323
123



324
450



325
341



326
220



327
314



328
424



329
395



330
355



331
287



332
183



333
234



334
125



335
342



336
452



337
397



338
432



339
316



340
345



341
241



342
207



343
403



344
357



345
187



346
236



347
126



348
242



349
398



350
346



351
456



352
358



353
405



354
303



355
189



356
215



357
361



358
244



359
348



360
419



361
406



362
311



363
219



364
409



365
362



366
464



367
421



368
369



369
190



370
248



371
231



372
410



373
364



374
335



375
422



376
315



377
221



378
370



379
425



380
235



381
451



382
480



383
412



384
343



385
222



386
317



387
372



388
426



389
453



390
237



391
433



392
347



393
243



394
454



395
318



396
376



397
428



398
238



399
359



400
457



401
399



402
349



403
434



404
363



405
245



406
458



407
127



408
407



409
436



410
465



411
350



412
246



413
460



414
249



415
411



416
365



417
440



418
466



419
371



420
423



421
366



422
250



423
413



424
468



425
481



426
191



427
373



428
427



429
414



430
252



431
482



432
472



433
223



434
374



435
429



436
455



437
377



438
435



439
484



440
319



441
430



442
239



443
378



444
459



445
437



446
488



447
380



448
461



449
496



450
438



451
467



452
247



453
351



454
441



455
462



456
469



457
442



458
251



459
367



460
483



461
470



462
444



463
473



464
253



465
485



466
415



467
375



468
474



469
254



470
486



471
489



472
431



473
379



474
476



475
490



476
497



477
439



478
381



479
463



480
492



481
498



482
382



483
443



484
471



485
445



486
500



487
446



488
255



489
504



490
475



491
487



492
477



493
491



494
478



495
493



496
383



497
499



498
494



499
501



500
502



501
447



502
505



503
506



504
508



505
479



506
495



507
503



508
507



509
509



510
510



511
511










Sequence Q23, having a sequence length of 256:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 6, 9, 17, 10, 18, 128, 12, 33, 20, 34, 24, 65, 36, 7, 129, 66, 11, 40, 68, 19, 13, 130, 48, 14, 72, 21, 132, 35, 26, 80, 37, 25, 22, 136, 96, 38, 67, 41, 144, 28, 69, 42, 49, 160, 70, 131, 44, 73, 192, 50, 74, 52, 15, 133, 81, 23, 134, 76, 137, 82, 56, 27, 97, 39, 84, 138, 145, 29, 43, 98, 88, 140, 30, 146, 71, 161, 45, 100, 51, 148, 46, 75, 104, 162, 53, 193, 152, 77, 164, 54, 83, 57, 112, 135, 78, 194, 85, 58, 168, 139, 99, 86, 60, 89, 196, 141, 101, 147, 176, 142, 90, 200, 31, 149, 102, 105, 163, 92, 47, 150, 208, 106, 153, 165, 55, 113, 154, 79, 108, 224, 166, 195, 169, 59, 114, 156, 87, 197, 116, 170, 61, 177, 91, 198, 172, 120, 201, 62, 143, 103, 178, 93, 202, 151, 209, 180, 107, 94, 204, 155, 210, 109, 184, 115, 167, 225, 157, 110, 117, 212, 171, 226, 216, 158, 118, 173, 121, 199, 179, 228, 122, 174, 203, 181, 63, 232, 124, 182, 205, 211, 185, 240, 206, 95, 213, 186, 111, 227, 214, 188, 217, 229, 159, 119, 218, 230, 233, 175, 123, 220, 183, 234, 125, 241, 207, 187, 236, 126, 242, 189, 215, 244, 219, 190, 248, 231, 221, 235, 222, 237, 243, 238, 245, 127, 246, 249, 250, 191, 252, 223, 239, 247, 251, 253, 254, 255]












TABLE Q23, having a sequence length of 256:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
64



10
6



11
9



12
17



13
10



14
18



15
128



16
12



17
33



18
20



19
34



20
24



21
65



22
36



23
7



24
129



25
66



26
11



27
40



28
68



29
19



30
13



31
130



32
48



33
14



34
72



35
21



36
132



37
35



38
26



39
80



40
37



41
25



42
22



43
136



44
96



45
38



46
67



47
41



48
144



49
28



50
69



51
42



52
49



53
160



54
70



55
131



56
44



57
73



58
192



59
50



60
74



61
52



62
15



63
133



64
81



65
23



66
134



67
76



68
137



69
82



70
56



71
27



72
97



73
39



74
84



75
138



76
145



77
29



78
43



79
98



80
88



81
140



82
30



83
146



84
71



85
161



86
45



87
100



88
51



89
148



90
46



91
75



92
104



93
162



94
53



95
193



96
152



97
77



98
164



99
54



100
83



101
57



102
112



103
135



104
78



105
194



106
85



107
58



108
168



109
139



110
99



111
86



112
60



113
89



114
196



115
141



116
101



117
147



118
176



119
142



120
90



121
200



122
31



123
149



124
102



125
105



126
163



127
92



128
47



129
150



130
208



131
106



132
153



133
165



134
55



135
113



136
154



137
79



138
108



139
224



140
166



141
195



142
169



143
59



144
114



145
156



146
87



147
197



148
116



149
170



150
61



151
177



152
91



153
198



154
172



155
120



156
201



157
62



158
143



159
103



160
178



161
93



162
202



163
151



164
209



165
180



166
107



167
94



168
204



169
155



170
210



171
109



172
184



173
115



174
167



175
225



176
157



177
110



178
117



179
212



180
171



181
226



182
216



183
158



184
118



185
173



186
121



187
199



188
179



189
228



190
122



191
174



192
203



193
181



194
63



195
232



196
124



197
182



198
205



199
211



200
185



201
240



202
206



203
95



204
213



205
186



206
111



207
227



208
214



209
188



210
217



211
229



212
159



213
119



214
218



215
230



216
233



217
175



218
123



219
220



220
183



221
234



222
125



223
241



224
207



225
187



226
236



227
126



228
242



229
189



230
215



231
244



232
219



233
190



234
248



235
231



236
221



237
235



238
222



239
237



240
243



241
238



242
245



243
127



244
246



245
249



246
250



247
191



248
252



249
223



250
239



251
247



252
251



253
253



254
254



255
255










Sequence Q24, having a sequence length of 128:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 6, 9, 17, 10, 18, 12, 33, 20, 34, 24, 65, 36, 7, 66, 11, 40, 68, 19, 13, 48, 14, 72, 21, 35, 26, 80, 37, 25, 22, 96, 38, 67, 41, 28, 69, 42, 49, 70, 44, 73, 50, 74, 52, 15, 81, 23, 76, 82, 56, 27, 97, 39, 84, 29, 43, 98, 88, 30, 71, 45, 100, 51, 46, 75, 104, 53, 77, 54, 83, 57, 112, 78, 85, 58, 99, 86, 60, 89, 101, 90, 31, 102, 105, 92, 47, 106, 55, 113, 79, 108, 59, 114, 87, 116, 61, 91, 120, 62, 103, 93, 107, 94, 109, 115, 110, 117, 118, 121, 122, 63, 124, 95, 111, 119, 123, 125, 126, 127]









TABLE Q24







having a sequence length of 128:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
64



10
6



11
9



12
17



13
10



14
18



15
12



16
33



17
20



18
34



19
24



20
65



21
36



22
7



23
66



24
11



25
40



26
68



27
19



28
13



29
48



30
14



31
72



32
21



33
35



34
26



35
80



36
37



37
25



38
22



39
96



40
38



41
67



42
41



43
28



44
69



45
42



46
49



47
70



48
44



49
73



50
50



51
74



52
52



53
15



54
81



55
23



56
76



57
82



58
56



59
27



60
97



61
39



62
84



63
29



64
43



65
98



66
88



67
30



68
71



69
45



70
100



71
51



72
46



73
75



74
104



75
53



76
77



77
54



78
83



79
57



80
112



81
78



82
85



83
58



84
99



85
86



86
60



87
89



88
101



89
90



90
31



91
102



92
105



93
92



94
47



95
106



96
55



97
113



98
79



99
108



100
59



101
114



102
87



103
116



104
61



105
91



106
120



107
62



108
103



109
93



110
107



111
94



112
109



113
115



114
110



115
117



116
118



117
121



118
122



119
63



120
124



121
95



122
111



123
119



124
123



125
125



126
126



127
127










Sequence Q25, having a sequence length of 64:

    • [0, 1, 2, 4, 8, 16, 32, 3, 5, 6, 9, 17, 10, 18, 12, 33, 20, 34, 24, 36, 7, 11, 40, 19, 13, 48, 14, 21, 35, 26, 37, 25, 22, 38, 41, 28, 42, 49, 44, 50, 52, 15, 23, 56, 27, 39, 29, 43, 30, 45, 51, 46, 53, 54, 57, 58, 60, 31, 47, 55, 59, 61, 62, 63]












Table Q25, having a sequence length of 64










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
2



3
4



4
8



5
16



6
32



7
3



8
5



9
6



10
9



11
17



12
10



13
18



14
12



15
33



16
20



17
34



18
24



19
36



20
7



21
11



22
40



23
19



24
13



25
48



26
14



27
21



28
35



29
26



30
37



31
25



32
22



33
38



34
41



35
28



36
42



37
49



38
44



39
50



40
52



41
15



42
23



43
56



44
27



45
39



46
29



47
43



48
30



49
45



50
51



51
46



52
53



53
54



54
57



55
58



56
60



57
31



58
47



59
55



60
59



61
61



62
62



63
63










Sequence Z21, having a sequence length of 1024:

    • [0, 1, 2, 7, 3, 8, 10, 24, 4, 11, 13, 28, 16, 32, 35, 76, 5, 12, 14, 31, 19, 38, 47, 80, 21, 46, 42, 87, 57, 95, 101, 167, 6, 17, 20, 40, 23, 45, 51, 89, 29, 55, 59, 96, 69, 108, 115, 177, 34, 61, 73, 112, 75, 123, 130, 190, 86, 133, 143, 210, 148, 218, 235, 327, 9, 22, 26, 54, 30, 58, 64, 103, 36, 71, 74, 116, 82, 126, 138, 197, 44, 79, 84, 131, 91, 141, 147, 214, 99, 149, 162, 228, 176, 242, 259, 364, 49, 88, 97, 146, 111, 154, 172, 239, 121, 173, 186, 257, 198, 271, 278, 369, 134, 192, 212, 273, 216, 283, 300, 401, 233, 307, 312, 417, 333, 435, 460, 585, 15, 25, 33, 68, 39, 77, 81, 137, 48, 83, 92, 145, 100, 153, 161, 236, 56, 93, 102, 159, 113, 168, 178, 254, 125, 187, 196, 266, 213, 277, 298, 394, 62, 107, 122, 175, 127, 189, 201, 274, 144, 207, 217, 286, 232, 306, 314, 416, 160, 221, 240, 309, 256, 322, 340, 433, 272, 348, 367, 453, 382, 471, 505, 619, 72, 124, 140, 205, 151, 215, 231, 308, 165, 234, 252, 320, 263, 344, 358, 449, 180, 255, 268, 346, 284, 366, 381, 473, 296, 390, 407, 486, 421, 519, 529, 639, 199, 275, 290, 379, 310, 392, 411, 510, 332, 412, 434, 522, 459, 535, 560, 670, 350, 448, 461, 552, 480, 583, 590, 695, 508, 593, 611, 707, 628, 728, 746, 816, 18, 37, 41, 90, 50, 94, 104, 166, 53, 105, 118, 184, 128, 200, 211, 293, 63, 119, 129, 208, 142, 206, 222, 303, 155, 223, 238, 311, 253, 330, 339, 432, 66, 139, 152, 209, 164, 226, 241, 323, 174, 249, 262, 345, 267, 355, 375, 468, 183, 265, 289, 363, 292, 387, 399, 484, 315, 406, 423, 518, 446, 530, 555, 665, 78, 169, 170, 251, 181, 258, 276, 361, 191, 288, 285, 386, 304, 400, 410, 513, 237, 297, 326, 403, 329, 420, 436, 528, 357, 447, 464, 550, 481, 573, 589, 699, 264, 325, 334, 431, 362, 452, 466, 561, 380, 478, 494, 582, 512, 596, 610, 708, 402, 503, 520, 608, 531, 620, 647, 732, 557, 660, 671, 756, 677, 778, 796, 854, 85, 182, 188, 291, 227, 305, 317, 404, 248, 313, 331, 428, 349, 444, 462, 568, 261, 347, 356, 451, 368, 467, 483, 586, 391, 491, 511, 595, 526, 612, 627, 731, 295, 365, 388, 482, 395, 501, 514, 609, 427, 521, 533, 624, 558, 648, 666, 755, 445, 546, 574, 662, 587, 673, 693, 777, 604, 701, 706, 800, 726, 804, 813, 881, 324, 389, 418, 523, 443, 534, 554, 649, 465, 567, 584, 672, 592, 678, 704, 780, 498, 588, 606, 694, 614, 705, 723, 803, 638, 727, 745, 821, 767, 834, 845, 913, 524, 616, 635, 720, 664, 730, 750, 824, 676, 754, 771, 842, 788, 850, 865, 926, 684, 776, 794, 860, 809, 870, 878, 935, 818, 885, 892, 946, 909, 954, 959, 988, 27, 43, 52, 98, 60, 106, 110, 193, 65, 114, 120, 202, 136, 219, 224, 338, 67, 135, 132, 220, 158, 243, 245, 354, 163, 260, 282, 370, 301, 393, 408, 532, 70, 156, 157, 246, 179, 280, 287, 383, 194, 302, 318, 424, 319, 422, 440, 536, 203, 321, 341, 437, 359, 455, 476, 562, 371, 469, 495, 579, 497, 599, 613, 735, 109, 171, 185, 294, 204, 328, 335, 426, 229, 343, 351, 454, 377, 475, 500, 570, 250, 353, 372, 470, 396, 496, 487, 594, 425, 488, 506, 615, 545, 632, 656, 752, 269, 384, 409, 490, 415, 515, 527, 625, 439, 544, 563, 645, 580, 667, 675, 775, 457, 559, 578, 674, 607, 685, 709, 799, 634, 719, 729, 806, 749, 819, 840, 905, 117, 195, 225, 342, 244, 352, 378, 477, 270, 373, 397, 489, 419, 507, 517, 621, 281, 405, 414, 516, 441, 541, 553, 640, 456, 564, 571, 669, 597, 683, 703, 779, 316, 430, 438, 556, 474, 575, 572, 679, 492, 591, 603, 698, 630, 716, 725, 805, 509, 617, 633, 717, 650, 740, 747, 825, 659, 753, 770, 837, 786, 852, 863, 925, 337, 463, 479, 598, 485, 605, 626, 712, 539, 631, 644, 738, 653, 744, 765, 833, 547, 651, 658, 748, 682, 769, 781, 847, 702, 787, 802, 866, 812, 877, 888, 942, 565, 687, 690, 772, 710, 791, 807, 871, 722, 810, 822, 884, 838, 894, 908, 953, 758, 829, 841, 901, 856, 912, 919, 962, 867, 922, 931, 969, 939, 975, 980, 1002, 150, 230, 247, 374, 279, 398, 413, 525, 299, 429, 442, 543, 458, 569, 577, 689, 336, 450, 472, 581, 493, 600, 602, 700, 504, 618, 636, 721, 646, 741, 751, 826, 360, 499, 502, 601, 538, 623, 637, 736, 542, 643, 655, 743, 663, 764, 773, 846, 548, 661, 681, 766, 696, 784, 797, 864, 718, 801, 811, 876, 828, 889, 903, 949, 376, 537, 540, 641, 549, 652, 668, 762, 576, 680, 692, 774, 713, 793, 808, 874, 629, 697, 714, 798, 724, 817, 827, 886, 760, 830, 844, 904, 855, 915, 920, 964, 654, 734, 742, 823, 761, 836, 849, 906, 783, 851, 862, 916, 873, 928, 934, 971, 795, 868, 880, 929, 890, 936, 944, 978, 902, 948, 956, 984, 963, 990, 994, 1009, 385, 551, 566, 688, 622, 691, 711, 792, 642, 715, 737, 820, 757, 832, 843, 899, 657, 739, 759, 835, 768, 848, 857, 914, 785, 861, 872, 924, 887, 932, 941, 977, 686, 763, 782, 858, 789, 869, 875, 927, 815, 883, 891, 937, 897, 945, 951, 983, 839, 895, 900, 947, 910, 955, 960, 989, 921, 965, 968, 995, 973, 998, 1000, 1014, 733, 790, 814, 882, 831, 893, 896, 943, 853, 898, 907, 952, 917, 957, 966, 992, 859, 911, 918, 961, 930, 967, 972, 997, 938, 974, 979, 1001, 985, 1004, 1006, 1017, 879, 923, 933, 970, 940, 976, 981, 1003, 950, 982, 986, 1005, 991, 1007, 1010, 1018, 958, 987, 993, 1008, 996, 1011, 1012, 1019, 999, 1013, 1015, 1020, 1016, 1021, 1022, 1023]









TABLE Z21







having a sequence length of 1024:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
10



7
24



8
4



9
11



10
13



11
28



12
16



13
32



14
35



15
76



16
5



17
12



18
14



19
31



20
19



21
38



22
47



23
80



24
21



25
46



26
42



27
87



28
57



29
95



30
101



31
167



32
6



33
17



34
20



35
40



36
23



37
45



38
51



39
89



40
29



41
55



42
59



43
96



44
69



45
108



46
115



47
177



48
34



49
61



50
73



54
130



55
190



56
86



57
133



58
143



59
210



60
148



61
218



62
235



63
327



64
9



65
22



66
26



67
54



68
30



69
58



70
64



71
103



72
36



73
71



74
74



75
116



76
82



77
126



78
138



79
197



80
44



81
79



82
84



83
131



84
91



85
141



89
149



90
162



91
228



92
176



93
242



94
259



95
364



96
49



97
88



98
97



99
146



100
111



101
154



102
172



103
239



104
121



105
173



106
186



107
257



108
198



109
271



110
278



111
369



112
134



113
192



114
212



115
273



116
216



117
283



118
300



119
401



120
233



124
333



125
435



126
460



127
585



128
15



129
25



130
33



131
68



132
39



133
77



134
81



135
137



136
48



137
83



138
92



139
145



140
100



141
153



142
161



143
236



144
56



145
93



146
102



147
159



148
113



149
168



150
178



151
254



152
125



153
187



154
196



155
266



156
213



157
277



158
298



159
394



160
62



161
107



162
122



163
175



164
127



165
189



166
201



167
274



168
144



169
207



170
217



171
286



172
232



173
306



174
314



175
416



176
160



177
221



178
240



182
340



183
433



184
272



185
348



186
367



187
453



188
382



189
471



190
505



191
619



192
72



193
124



194
140



195
205



196
151



197
215



198
231



199
308



200
165



201
234



202
252



203
320



204
263



205
344



206
358



207
449



208
180



209
255



210
268



211
346



212
284



213
366



217
390



218
407



219
486



220
421



221
519



222
529



223
639



224
199



225
275



226
290



227
379



228
310



229
392



230
411



231
510



232
332



233
412



234
434



235
522



236
459



237
535



238
560



239
670



240
350



241
448



242
461



243
552



244
480



245
583



246
590



247
695



248
508



252
628



253
728



254
746



255
816



256
18



257
37



258
41



259
90



260
50



261
94



262
104



263
166



264
53



265
105



266
118



267
184



268
128



269
200



270
211



271
293



272
63



273
119



274
129



275
208



276
142



277
206



278
222



279
303



280
155



281
223



282
238



283
311



284
253



285
330



286
339



287
432



288
66



289
139



290
152



291
209



292
164



293
226



294
241



295
323



296
174



297
249



298
262



299
345



300
267



301
355



302
375



303
468



304
183



305
265



306
289



310
399



311
484



312
315



313
406



314
423



315
518



316
446



317
530



318
555



319
665



320
78



321
169



322
170



323
251



324
181



325
258



326
276



327
361



328
191



329
288



330
285



331
386



332
304



333
400



334
410



335
513



336
237



337
297



338
326



339
403



340
329



341
420



345
447



346
464



347
550



348
481



349
573



350
589



351
699



352
264



353
325



354
334



355
431



356
362



357
452



358
466



359
561



360
380



361
478



362
494



363
582



364
512



365
596



366
610



367
708



368
402



369
503



370
520



371
608



372
531



373
620



374
647



375
732



376
557



380
677



381
778



382
796



383
854



384
85



385
182



386
188



387
291



388
227



389
305



390
317



391
404



392
248



393
313



394
331



395
428



396
349



397
444



398
462



399
568



400
261



401
347



402
356



403
451



404
368



405
467



406
483



407
586



408
391



409
491



410
511



411
595



412
526



413
612



414
627



415
731



416
295



417
365



418
388



419
482



420
395



421
501



422
514



423
609



424
427



425
521



426
533



427
624



428
558



429
648



430
666



431
755



432
445



433
546



434
574



438
693



439
777



440
604



441
701



442
706



443
800



444
726



445
804



446
813



447
881



448
324



449
389



450
418



451
523



452
443



453
534



454
554



455
649



456
465



457
567



458
584



459
672



460
592



461
678



462
704



463
780



464
498



465
588



466
606



467
694



468
614



469
705



473
727



474
745



475
821



476
767



477
834



478
845



479
913



480
524



481
616



482
635



483
720



484
664



485
730



486
750



487
824



488
676



489
754



490
771



491
842



492
788



493
850



494
865



495
926



496
684



497
776



498
794



499
860



500
809



501
870



502
878



503
935



504
818



508
909



509
954



510
959



511
988



512
27



513
43



514
52



515
98



516
60



517
106



518
110



519
193



520
65



521
114



522
120



523
202



524
136



525
219



526
224



527
338



528
67



529
135



530
132



531
220



532
158



533
243



534
245



535
354



536
163



537
260



538
282



539
370



540
301



541
393



542
408



543
532



544
70



545
156



546
157



547
246



548
179



549
280



550
287



551
383



552
194



553
302



554
318



555
424



556
319



557
422



558
440



559
536



560
203



561
321



562
341



566
476



567
562



568
371



569
469



570
495



571
579



572
497



573
599



574
613



575
735



576
109



577
171



578
185



579
294



580
204



581
328



582
335



583
426



584
229



585
343



586
351



587
454



588
377



589
475



590
500



591
570



592
250



593
353



594
372



595
470



596
396



597
496



601
488



602
506



603
615



604
545



605
632



606
656



607
752



608
269



609
384



610
409



611
490



612
415



613
515



614
527



615
625



616
439



617
544



618
563



619
645



620
580



621
667



622
675



623
775



624
457



625
559



626
578



627
674



628
607



629
685



630
709



631
799



632
634



636
749



637
819



638
840



639
905



640
117



641
195



642
225



643
342



644
244



645
352



646
378



647
477



648
270



649
373



650
397



651
489



652
419



653
507



654
517



655
621



656
281



657
405



658
414



659
516



660
441



661
541



662
553



663
640



664
456



665
564



666
571



667
669



668
597



669
683



670
703



671
779



672
316



673
430



674
438



675
556



676
474



677
575



678
572



679
679



680
492



681
591



682
603



683
698



684
630



685
716



686
725



687
805



688
509



689
617



690
633



694
747



695
825



696
659



697
753



698
770



699
837



700
786



701
852



702
863



703
925



704
337



705
463



706
479



707
598



708
485



709
605



710
626



711
712



712
539



713
631



714
644



715
738



716
653



717
744



718
765



719
833



720
547



721
651



722
658



723
748



724
682



725
769



729
787



730
802



731
866



732
812



733
877



734
888



735
942



736
565



737
687



738
690



739
772



740
710



741
791



742
807



743
871



744
722



745
810



746
822



747
884



748
838



749
894



750
908



751
953



752
758



753
829



754
841



755
901



756
856



757
912



758
919



759
962



760
867



764
939



765
975



766
980



767
1002



768
150



769
230



770
247



771
374



772
279



773
398



774
413



775
525



776
299



777
429



778
442



779
543



780
458



781
569



782
577



783
689



784
336



785
450



786
472



787
581



788
493



789
600



790
602



791
700



792
504



793
618



794
636



795
721



796
646



797
741



798
751



799
826



800
360



801
499



802
502



803
601



804
538



805
623



806
637



807
736



808
542



809
643



810
655



811
743



812
663



813
764



814
773



815
846



816
548



817
661



818
681



822
797



823
864



824
718



825
801



826
811



827
876



828
828



829
889



830
903



831
949



832
376



833
537



834
540



835
641



836
549



837
652



838
668



839
762



840
576



841
680



842
692



843
774



844
713



845
793



846
808



847
874



848
629



849
697



850
714



851
798



852
724



853
817



857
830



858
844



859
904



860
855



861
915



862
920



863
964



864
654



865
734



866
742



867
823



868
761



869
836



870
849



871
906



872
783



873
851



874
862



875
916



876
873



877
928



878
934



879
971



880
795



881
868



882
880



883
929



884
890



885
936



886
944



887
978



888
902



892
963



893
990



894
994



895
1009



896
385



897
551



898
566



899
688



900
622



901
691



902
711



903
792



904
642



905
715



906
737



907
820



908
757



909
832



910
843



911
899



912
657



913
739



914
759



915
835



916
768



917
848



918
857



919
914



920
785



921
861



922
872



923
924



924
887



925
932



926
941



927
977



928
686



929
763



930
782



931
858



932
789



933
869



934
875



935
927



936
815



937
883



938
891



939
937



940
897



941
945



942
951



943
983



944
839



945
895



946
900



950
960



951
989



952
921



953
965



954
968



955
995



956
973



957
998



958
1000



959
1014



960
733



961
790



962
814



963
882



964
831



965
893



966
896



967
943



968
853



969
898



970
907



971
952



972
917



973
957



974
966



975
992



976
859



977
911



978
918



979
961



980
930



981
967



985
974



986
979



987
1001



988
985



989
1004



990
1006



991
1017



992
879



993
923



994
933



995
970



996
940



997
976



998
981



999
1003



1000
950



1001
982



1002
986



1003
1005



1004
991



1005
1007



1006
1010



1007
1018



1008
958



1009
987



1010
993



1011
1008



1012
996



1013
1011



1014
1012



1015
1019



1016
999



1020
1016



1021
1021



1022
1022



1023
1023










Sequence Z22, having a sequence length of 512:

    • [0, 1, 2, 7, 3, 8, 10, 24, 4, 11, 13, 27, 16, 31, 34, 69, 5, 12, 14, 30, 19, 37, 45, 73, 21, 44, 41, 80, 54, 88, 93, 145, 6, 17, 20, 39, 23, 43, 49, 82, 28, 52, 56, 89, 63, 99, 103, 154, 33, 57, 66, 101, 68, 109, 116, 165, 79, 118, 126, 179, 131, 187, 198, 268, 9, 22, 26, 51, 29, 55, 60, 95, 35, 64, 67, 104, 75, 112, 121, 169, 42, 72, 77, 117, 84, 124, 130, 183, 91, 132, 141, 193, 153, 205, 216, 291, 47, 81, 90, 129, 100, 136, 149, 202, 107, 150, 161, 214, 170, 225, 232, 296, 119, 167, 181, 227, 185, 233, 247, 313, 196, 252, 257, 323, 273, 334, 347, 407, 15, 25, 32, 62, 38, 70, 74, 120, 46, 76, 85, 128, 92, 135, 140, 199, 53, 86, 94, 138, 102, 146, 155, 211, 111, 162, 168, 222, 182, 231, 246, 309, 58, 98, 108, 152, 113, 164, 173, 228, 127, 176, 186, 236, 195, 251, 259, 322, 139, 188, 203, 254, 213, 263, 276, 332, 226, 281, 294, 345, 301, 355, 369, 426, 65, 110, 123, 174, 133, 184, 194, 253, 143, 197, 209, 262, 219, 277, 287, 342, 156, 212, 224, 279, 234, 293, 300, 356, 244, 306, 318, 363, 326, 377, 385, 433, 171, 229, 239, 298, 255, 308, 320, 371, 272, 321, 333, 380, 346, 390, 398, 442, 283, 341, 348, 393, 358, 405, 412, 452, 370, 414, 422, 458, 430, 464, 469, 488, 18, 36, 40, 83, 48, 87, 96, 144, 50, 97, 105, 160, 114, 172, 180, 242, 59, 106, 115, 177, 125, 175, 189, 248, 137, 190, 201, 256, 210, 270, 275, 331, 61, 122, 134, 178, 142, 191, 204, 264, 151, 207, 218, 278, 223, 284, 297, 354, 159, 221, 238, 290, 241, 303, 311, 362, 260, 317, 327, 376, 339, 386, 395, 440, 71, 147, 148, 208, 157, 215, 230, 288, 166, 237, 235, 302, 249, 312, 319, 374, 200, 245, 267, 315, 269, 325, 335, 384, 286, 340, 350, 392, 359, 402, 411, 453, 220, 266, 274, 330, 289, 344, 352, 399, 299, 357, 365, 404, 373, 416, 421, 459, 314, 368, 378, 419, 387, 427, 434, 467, 396, 437, 443, 473, 447, 478, 482, 496, 78, 158, 163, 240, 192, 250, 261, 316, 206, 258, 271, 329, 282, 337, 349, 401, 217, 280, 285, 343, 295, 353, 361, 408, 307, 364, 372, 415, 383, 423, 429, 466, 243, 292, 304, 360, 310, 367, 375, 420, 328, 379, 388, 428, 397, 435, 441, 472, 338, 391, 403, 438, 409, 445, 450, 477, 417, 454, 457, 483, 462, 485, 487, 501, 265, 305, 324, 381, 336, 389, 394, 436, 351, 400, 406, 444, 413, 448, 455, 479, 366, 410, 418, 451, 424, 456, 461, 484, 432, 463, 468, 490, 474, 492, 494, 505, 382, 425, 431, 460, 439, 465, 470, 491, 446, 471, 475, 493, 480, 495, 498, 506, 449, 476, 481, 497, 486, 499, 500, 507, 489, 502, 503, 508, 504, 509, 510, 511]












TABLE Z22, having a sequence length of 512:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
10



7
24



8
4



9
11



10
13



11
27



12
16



13
31



14
34



15
69



16
5



17
12



18
14



19
30



20
19



21
37



22
45



23
73



24
21



25
44



26
41



27
80



28
54



29
88



30
93



31
145



32
6



33
17



34
20



35
39



36
23



37
43



38
49



39
82



40
28



41
52



42
56



43
89



44
63



45
99



46
103



47
154



48
33



49
57



50
66



51
101



52
68



53
109



54
116



55
165



56
79



57
118



58
126



59
179



60
131



61
187



62
198



63
268



64
9



65
22



66
26



67
51



68
29



69
55



70
60



71
95



72
35



73
64



74
67



75
104



76
75



77
112



78
121



79
169



80
42



81
72



82
77



83
117



84
84



85
124



86
130



87
183



88
91



89
132



90
141



91
193



92
153



93
205



94
216



95
291



96
47



97
81



98
90



99
129



100
100



101
136



102
149



103
202



104
107



105
150



106
161



107
214



108
170



109
225



110
232



111
296



112
119



113
167



114
181



115
227



116
185



117
233



118
247



119
313



120
196



121
252



122
257



123
323



124
273



125
334



126
347



127
407



128
15



129
25



130
32



131
62



132
38



133
70



134
74



135
120



136
46



137
76



138
85



139
128



140
92



141
135



142
140



143
199



144
53



145
86



146
94



147
138



148
102



149
146



150
155



151
211



152
111



153
162



154
168



155
222



156
182



157
231



158
246



159
309



160
58



161
98



162
108



163
152



164
113



165
164



166
173



167
228



168
127



169
176



170
186



171
236



172
195



173
251



174
259



175
322



176
139



177
188



178
203



179
254



180
213



181
263



182
276



183
332



184
226



185
281



186
294



187
345



188
301



189
355



190
369



191
426



192
65



193
110



194
123



195
174



196
133



197
184



198
194



199
253



200
143



201
197



202
209



203
262



204
219



205
277



206
287



207
342



208
156



209
212



210
224



211
279



212
234



213
293



214
300



215
356



216
244



217
306



218
318



219
363



220
326



221
377



222
385



223
433



224
171



225
229



226
239



227
298



228
255



229
308



230
320



231
371



232
272



233
321



234
333



235
380



236
346



237
390



238
398



239
442



240
283



241
341



242
348



243
393



244
358



245
405



246
412



247
452



248
370



249
414



250
422



251
458



252
430



253
464



254
469



255
488



256
18



257
36



258
40



259
83



260
48



261
87



262
96



263
144



264
50



265
97



266
105



267
160



268
114



269
172



270
180



271
242



272
59



273
106



274
115



275
177



276
125



277
175



278
189



279
248



280
137



281
190



282
201



283
256



284
210



285
270



286
275



287
331



288
61



289
122



290
134



291
178



292
142



293
191



294
204



295
264



296
151



297
207



298
218



299
278



300
223



301
284



302
297



303
354



304
159



305
221



306
238



307
290



308
241



309
303



310
311



311
362



312
260



313
317



314
327



315
376



316
339



317
386



318
395



319
440



320
71



321
147



322
148



323
208



324
157



325
215



326
230



327
288



328
166



329
237



330
235



331
302



332
249



333
312



334
319



335
374



336
200



337
245



338
267



339
315



340
269



341
325



342
335



343
384



344
286



345
340



346
350



347
392



348
359



349
402



350
411



351
453



352
220



353
266



354
274



355
330



356
289



357
344



358
352



359
399



360
299



361
357



362
365



363
404



364
373



365
416



366
421



367
459



368
314



369
368



370
378



371
419



372
387



373
427



374
434



375
467



376
396



377
437



378
443



379
473



380
447



381
478



382
482



383
496



384
78



385
158



386
163



387
240



388
192



389
250



390
261



391
316



392
206



393
258



394
271



395
329



396
282



397
337



398
349



399
401



400
217



401
280



402
285



403
343



404
295



405
353



406
361



407
408



408
307



409
364



410
372



411
415



412
383



413
423



414
429



415
466



416
243



417
292



418
304



419
360



420
310



421
367



422
375



423
420



424
328



425
379



426
388



427
428



428
397



429
435



430
441



431
472



432
338



433
391



434
403



435
438



436
409



437
445



438
450



439
477



440
417



441
454



442
457



443
483



444
462



445
485



446
487



447
501



448
265



449
305



450
324



451
381



452
336



453
389



454
394



455
436



456
351



457
400



458
406



459
444



460
413



461
448



462
455



463
479



464
366



465
410



466
418



467
451



468
424



469
456



470
461



471
484



472
432



473
463



474
468



475
490



476
474



477
492



478
494



479
505



480
382



481
425



482
431



483
460



484
439



485
465



486
470



487
491



488
446



489
471



490
475



491
493



492
480



493
495



494
498



495
506



496
449



497
476



498
481



499
497



500
486



501
499



502
500



503
507



504
489



505
502



506
503



507
508



508
504



509
509



510
510



511
511










Sequence Z23, having a sequence length of 256:

    • [0, 1, 2, 7, 3, 8, 10, 23, 4, 11, 13, 26, 16, 30, 33, 62, 5, 12, 14, 29, 18, 35, 42, 65, 20, 41, 38, 71, 49, 77, 82, 122, 6, 17, 19, 37, 22, 40, 45, 73, 27, 47, 51, 78, 56, 86, 90, 128, 32, 52, 59, 88, 61, 94, 99, 134, 70, 101, 107, 143, 112, 150, 157, 194, 9, 21, 25, 46, 28, 50, 54, 84, 34, 57, 60, 91, 67, 97, 104, 137, 39, 64, 69, 100, 74, 106, 111, 146, 80, 113, 120, 152, 127, 161, 167, 203, 44, 72, 79, 110, 87, 116, 124, 159, 92, 125, 131, 166, 138, 171, 177, 206, 102, 135, 144, 173, 148, 178, 184, 213, 155, 186, 190, 218, 196, 222, 227, 243, 15, 24, 31, 55, 36, 63, 66, 103, 43, 68, 75, 109, 81, 115, 119, 158, 48, 76, 83, 117, 89, 123, 129, 163, 96, 132, 136, 169, 145, 176, 183, 212, 53, 85, 93, 126, 98, 133, 140, 174, 108, 142, 149, 180, 154, 185, 191, 217, 118, 151, 160, 188, 165, 193, 197, 220, 172, 200, 205, 225, 209, 229, 233, 247, 58, 95, 105, 141, 114, 147, 153, 187, 121, 156, 162, 192, 168, 198, 202, 224, 130, 164, 170, 199, 179, 204, 208, 230, 182, 210, 214, 232, 219, 236, 238, 249, 139, 175, 181, 207, 189, 211, 215, 235, 195, 216, 221, 237, 226, 239, 241, 250, 201, 223, 228, 240, 231, 242, 244, 251, 234, 245, 246, 252, 248, 253, 254, 255]









TABLE Z23







having a sequence length of 256:










Polarized
Reliability



channel
or sequence



sequence
number of



number
reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
10



7
23



8
4



9
11



10
13



11
26



12
16



13
30



14
33



15
62



16
5



17
12



18
14



19
29



20
18



21
35



22
42



23
65



24
20



25
41



26
38



27
71



28
49



29
77



30
82



31
122



32
6



33
17



34
19



35
37



36
22



37
40



38
45



39
73



40
27



41
47



42
51



43
78



44
56



45
86



46
90



47
128



48
32



49
52



50
59



51
88



52
61



53
94



54
99



55
134



56
70



57
101



58
107



59
143



60
112



61
150



62
157



63
194



64
9



65
21



66
25



67
46



68
28



69
50



70
54



71
84



72
34



73
57



74
60



75
91



76
67



77
97



78
104



79
137



80
39



81
64



82
69



83
100



84
74



85
106



86
111



87
146



88
80



89
113



90
120



91
152



92
127



93
161



94
167



95
203



96
44



97
72



98
79



99
110



100
87



101
116



102
124



103
159



104
92



105
125



106
131



107
166



108
138



109
171



110
177



111
206



112
102



113
135



114
144



115
173



116
148



117
178



118
184



119
213



120
155



121
186



122
190



123
218



124
196



125
222



126
227



127
243



128
15



129
24



130
31



131
55



132
36



133
63



134
66



135
103



136
43



137
68



138
75



139
109



140
81



141
115



142
119



143
158



144
48



145
76



146
83



147
117



148
89



149
123



150
129



151
163



152
96



153
132



154
136



155
169



156
145



157
176



158
183



159
212



160
53



161
85



162
93



163
126



164
98



165
133



166
140



167
174



168
108



169
142



170
149



171
180



172
154



173
185



174
191



175
217



176
118



177
151



178
160



179
188



180
165



181
193



182
197



183
220



184
172



185
200



186
205



187
225



188
209



189
229



190
233



191
247



192
58



193
95



194
105



195
141



196
114



197
147



198
153



199
187



200
121



201
156



202
162



203
192



204
168



205
198



206
202



207
224



208
130



209
164



210
170



211
199



212
179



213
204



214
208



215
230



216
182



217
210



218
214



219
232



220
219



221
236



222
238



223
249



224
139



225
175



226
181



227
207



228
189



229
211



230
215



231
235



232
195



233
216



234
221



235
237



236
226



237
239



238
241



239
250



240
201



241
223



242
228



243
240



244
231



245
242



246
244



247
251



248
234



249
245



250
246



251
252



252
248



253
253



254
254



255
255










Sequence Z24, having a sequence length of 128:

    • [0, 1, 2, 7, 3, 8, 10, 22, 4, 11, 13, 24, 15, 28, 30, 53, 5, 12, 14, 27, 17, 32, 38, 55, 19, 37, 34, 59, 43, 63, 67, 90, 6, 16, 18, 33, 21, 36, 40, 61, 25, 42, 45, 64, 48, 69, 72, 94, 29, 46, 50, 71, 52, 75, 77, 96, 58, 79, 83, 100, 86, 104, 107, 119, 9, 20, 23, 41, 26, 44, 47, 68, 31, 49, 51, 73, 56, 76, 81, 98, 35, 54, 57, 78, 62, 82, 85, 102, 66, 87, 89, 105, 93, 109, 111, 121, 39, 60, 65, 84, 70, 88, 91, 108, 74, 92, 95, 110, 99, 112, 114, 122, 80, 97, 101, 113, 103, 115, 116, 123, 106, 117, 118, 124, 120, 125, 126, 127]









TABLE Z24







having a length of 128.










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
10



7
22



8
4



9
11



10
13



11
24



12
15



13
28



14
30



15
53



16
5



17
12



18
14



19
27



20
17



21
32



22
38



23
55



24
19



25
37



26
34



27
59



28
43



29
63



30
67



31
90



32
6



33
16



34
18



35
33



36
21



37
36



38
40



39
61



40
25



41
42



42
45



43
64



44
48



45
69



46
72



47
94



48
29



49
46



50
50



51
71



52
52



53
75



54
77



55
96



56
58



57
79



58
83



59
100



60
86



61
104



62
107



63
119



64
9



65
20



66
23



67
41



68
26



69
44



70
47



71
68



72
31



73
49



74
51



75
73



76
56



77
76



78
81



79
98



80
35



81
54



82
57



83
78



84
62



85
82



86
85



87
102



88
66



89
87



90
89



91
105



92
93



93
109



94
111



95
121



96
39



97
60



98
65



99
84



100
70



101
88



102
91



103
108



104
74



105
92



106
95



107
110



108
99



109
112



110
114



111
122



112
80



113
97



114
101



115
113



116
103



117
115



118
116



119
123



120
106



121
117



122
118



123
124



124
120



125
125



126
126



127
127










Sequence Z25, having a sequence length of 64:

    • [0, 1, 2, 7, 3, 8, 9, 20, 4, 10, 12, 21, 14, 24, 26, 41, 5, 11, 13, 23, 16, 27, 32, 42, 18, 31, 29, 44, 35, 46, 48, 57, 6, 15, 17, 28, 19, 30, 33, 45, 22, 34, 36, 47, 38, 49, 51, 58, 25, 37, 39, 50, 40, 52, 53, 59, 43, 54, 55, 60, 56, 61, 62, 63]









TABLE Z25







having a sequence length of 64:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
2



3
7



4
3



5
8



6
9



7
20



8
4



9
10



10
12



11
21



12
14



13
24



14
26



15
41



16
5



17
11



18
13



19
23



20
16



21
27



22
32



23
42



24
18



25
31



26
29



27
44



28
35



29
46



30
48



31
57



32
6



33
15



34
17



35
28



36
19



37
30



38
33



39
45



40
22



41
34



42
36



43
47



44
38



45
49



46
51



47
58



48
25



49
37



50
39



51
50



52
40



53
52



54
53



55
59



56
43



57
54



58
55



59
60



60
56



61
61



62
62



63
63










Sixth group of sequences (a criterion that considers optimal performance of List 4).


Sequence Q26, having a sequence length of 1024:

    • [0, 1, 4, 8, 2, 16, 32, 6, 64, 512, 3, 12, 5, 18, 128, 9, 33, 17, 10, 36, 66, 24, 256, 20, 65, 34, 7, 129, 40, 11, 72, 132, 513, 19, 48, 68, 13, 257, 14, 21, 130, 26, 80, 35, 258, 38, 136, 96, 22, 516, 37, 25, 67, 264, 41, 144, 28, 69, 260, 49, 74, 160, 42, 520, 134, 70, 44, 81, 272, 15, 50, 131, 192, 73, 23, 514, 137, 52, 288, 76, 133, 82, 27, 97, 259, 39, 528, 56, 138, 84, 29, 145, 261, 43, 320, 544, 98, 140, 265, 30, 88, 146, 262, 100, 518, 161, 71, 45, 273, 51, 148, 266, 576, 46, 75, 104, 164, 193, 53, 162, 515, 384, 268, 77, 152, 54, 85, 524, 289, 112, 274, 57, 78, 135, 517, 194, 83, 290, 168, 276, 86, 530, 58, 139, 322, 196, 101, 640, 60, 147, 176, 280, 99, 89, 521, 292, 141, 321, 200, 90, 545, 31, 142, 102, 263, 529, 47, 386, 105, 296, 208, 522, 153, 92, 149, 267, 548, 163, 324, 113, 150, 578, 165, 55, 304, 106, 275, 536, 269, 385, 154, 768, 79, 108, 224, 166, 532, 59, 169, 114, 195, 577, 328, 270, 277, 87, 546, 156, 116, 388, 519, 336, 291, 278, 197, 641, 61, 177, 170, 552, 91, 281, 201, 198, 523, 62, 143, 294, 584, 172, 392, 103, 644, 120, 293, 282, 531, 352, 178, 202, 560, 323, 297, 93, 580, 107, 151, 209, 525, 284, 180, 400, 769, 94, 204, 298, 526, 326, 155, 533, 305, 109, 325, 642, 210, 184, 225, 538, 167, 300, 592, 115, 387, 329, 547, 110, 416, 770, 212, 271, 117, 550, 306, 157, 648, 226, 171, 330, 608, 337, 389, 534, 308, 216, 549, 121, 390, 537, 158, 279, 332, 579, 118, 173, 776, 338, 179, 553, 199, 353, 656, 283, 312, 540, 448, 228, 581, 393, 122, 181, 772, 232, 295, 561, 174, 394, 586, 63, 203, 672, 354, 554, 401, 340, 646, 124, 285, 582, 182, 299, 556, 240, 211, 593, 286, 344, 784, 396, 205, 527, 95, 418, 562, 185, 643, 213, 402, 704, 307, 327, 585, 356, 535, 206, 186, 649, 301, 111, 564, 302, 800, 360, 227, 588, 417, 159, 645, 404, 594, 309, 214, 539, 449, 331, 609, 119, 771, 217, 188, 551, 229, 568, 333, 408, 650, 310, 596, 339, 420, 541, 218, 657, 368, 773, 123, 230, 555, 175, 832, 391, 313, 610, 241, 652, 450, 334, 777, 220, 542, 341, 600, 424, 314, 658, 183, 774, 233, 612, 355, 673, 125, 287, 583, 395, 557, 234, 785, 316, 345, 563, 187, 660, 452, 778, 403, 558, 342, 397, 587, 207, 616, 236, 676, 432, 705, 346, 565, 361, 674, 126, 242, 896, 357, 780, 405, 589, 215, 664, 398, 566, 303, 597, 358, 801, 419, 624, 456, 786, 348, 189, 569, 244, 590, 410, 647, 219, 706, 311, 595, 362, 802, 464, 680, 406, 788, 421, 598, 231, 570, 248, 651, 369, 834, 190, 708, 409, 613, 315, 572, 364, 659, 422, 335, 221, 688, 451, 792, 370, 611, 425, 601, 235, 804, 343, 653, 412, 833, 480, 712, 222, 602, 317, 543, 453, 654, 426, 614, 372, 775, 433, 559, 237, 898, 617, 347, 808, 243, 720, 454, 665, 318, 604, 376, 661, 428, 779, 238, 675, 359, 836, 458, 625, 399, 662, 677, 245, 567, 434, 816, 457, 618, 349, 787, 465, 781, 897, 363, 666, 407, 591, 127, 620, 246, 736, 436, 678, 571, 350, 681, 249, 626, 460, 707, 840, 411, 782, 365, 789, 440, 599, 374, 668, 628, 423, 900, 466, 848, 803, 250, 790, 371, 709, 191, 573, 689, 481, 682, 413, 603, 793, 366, 713, 468, 710, 429, 574, 655, 252, 806, 414, 684, 904, 373, 615, 482, 632, 805, 223, 794, 864, 427, 690, 472, 714, 835, 455, 809, 377, 605, 619, 435, 663, 721, 319, 796, 430, 692, 912, 239, 606, 716, 461, 810, 484, 838, 667, 378, 817, 621, 437, 837, 722, 247, 696, 380, 737, 679, 459, 812, 627, 488, 899, 841, 441, 622, 928, 351, 724, 783, 469, 629, 818, 438, 669, 462, 738, 683, 251, 842, 849, 496, 901, 820, 728, 467, 633, 902, 367, 670, 791, 442, 844, 630, 474, 685, 850, 483, 691, 711, 379, 865, 795, 415, 824, 960, 740, 253, 905, 634, 444, 693, 744, 485, 807, 686, 906, 470, 575, 715, 375, 866, 913, 473, 852, 636, 797, 431, 694, 811, 486, 752, 723, 798, 489, 856, 908, 254, 717, 607, 930, 476, 697, 725, 914, 439, 819, 839, 868, 492, 718, 698, 381, 813, 623, 814, 498, 872, 739, 929, 445, 671, 916, 821, 463, 726, 961, 843, 490, 631, 729, 700, 382, 741, 845, 920, 471, 822, 851, 932, 730, 497, 880, 635, 742, 443, 687, 903, 825, 475, 753, 962, 846, 732, 500, 853, 936, 826, 446, 695, 745, 867, 637, 487, 799, 907, 746, 828, 493, 857, 699, 964, 915, 477, 854, 909, 719, 504, 748, 944, 858, 873, 638, 478, 754, 869, 917, 727, 499, 910, 815, 870, 931, 255, 968, 860, 701, 756, 922, 491, 731, 823, 874, 976, 918, 502, 933, 743, 760, 881, 494, 702, 921, 827, 876, 934, 847, 505, 733, 963, 882, 937, 747, 383, 855, 924, 992, 734, 829, 965, 501, 938, 884, 945, 749, 859, 755, 479, 966, 830, 888, 940, 750, 871, 506, 970, 911, 757, 946, 969, 861, 977, 447, 875, 919, 639, 758, 948, 862, 761, 508, 972, 923, 877, 952, 886, 935, 978, 762, 503, 883, 703, 993, 925, 878, 980, 941, 764, 495, 926, 885, 994, 735, 939, 984, 967, 889, 947, 831, 507, 942, 751, 973, 996, 890, 949, 759, 892, 971, 1000, 953, 509, 863, 981, 950, 974, 763, 1008, 979, 879, 954, 986, 995, 891, 927, 510, 765, 956, 997, 982, 887, 985, 943, 998, 1001, 766, 988, 951, 1004, 893, 1010, 957, 975, 511, 1002, 894, 983, 1009, 955, 987, 1012, 958, 999, 1005, 989, 1016, 990, 1011, 767, 1003, 1014, 1006, 1017, 895, 1013, 991, 1018, 959, 1020, 1015, 1007, 1019, 1021, 1022, 1023]









TABLE Q26







having a sequence length of 1024:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
4



3
8



4
2



5
16



6
32



7
6



8
64



9
512



10
3



11
12



12
5



13
18



14
128



15
9



16
33



17
17



18
10



19
36



20
66



21
24



22
256



23
20



24
65



25
34



26
7



27
129



28
40



29
11



30
72



31
132



32
513



33
19



34
48



35
68



36
13



37
257



38
14



39
21



40
130



44
258



45
38



46
136



47
96



48
22



49
516



50
37



51
25



52
67



53
264



54
41



55
144



56
28



57
69



58
260



59
49



60
74



61
160



62
42



63
520



64
134



65
70



66
44



67
81



68
272



69
15



70
50



71
131



72
192



73
73



74
23



75
514



79
76



80
133



81
82



82
27



83
97



84
259



85
39



86
528



87
56



88
138



89
84



90
29



91
145



92
261



93
43



94
320



95
544



96
98



97
140



98
265



99
30



100
88



101
146



102
262



103
100



104
518



105
161



106
71



107
45



108
273



109
51



110
148



114
75



115
104



116
164



117
193



118
53



119
162



120
515



121
384



122
268



123
77



124
152



125
54



126
85



127
524



128
289



129
112



130
274



131
57



132
78



133
135



134
517



135
194



136
83



137
290



138
168



139
276



140
86



141
530



142
58



143
139



144
322



145
196



146
101



147
640



148
60



149
147



150
176



151
280



152
99



153
89



154
521



155
292



156
141



157
321



158
200



159
90



160
545



161
31



162
142



163
102



164
263



165
529



166
47



167
386



168
105



172
153



173
92



174
149



175
267



176
548



177
163



178
324



179
113



180
150



181
578



182
165



183
55



184
304



185
106



186
275



187
536



188
269



189
385



190
154



191
768



192
79



193
108



194
224



195
166



196
532



197
59



198
169



199
114



200
195



201
577



202
328



203
270



207
156



208
116



209
388



210
519



211
336



212
291



213
278



214
197



215
641



216
61



217
177



218
170



219
552



220
91



221
281



222
201



223
198



224
523



225
62



226
143



227
294



228
584



229
172



230
392



231
103



232
644



233
120



234
293



235
282



236
531



237
352



238
178



242
297



243
93



244
580



245
107



246
151



247
209



248
525



249
284



250
180



251
400



252
769



253
94



254
204



255
298



256
526



257
326



258
155



259
533



260
305



261
109



262
325



263
642



264
210



265
184



266
225



267
538



268
167



269
300



270
592



271
115



272
387



273
329



274
547



275
110



276
416



277
770



278
212



279
271



280
117



281
550



282
306



283
157



284
648



285
226



286
171



287
330



288
608



289
337



290
389



291
534



292
308



293
216



294
549



295
121



296
390



300
332



301
579



302
118



303
173



304
776



305
338



306
179



307
553



308
199



309
353



310
656



311
283



312
312



313
540



314
448



315
228



316
581



317
393



318
122



319
181



320
772



321
232



322
295



323
561



324
174



325
394



326
586



327
63



328
203



329
672



330
354



331
554



335
124



336
285



337
582



338
182



339
299



340
556



341
240



342
211



343
593



344
286



345
344



346
784



347
396



348
205



349
527



350
95



351
418



352
562



353
185



354
643



355
213



356
402



357
704



358
307



359
327



360
585



361
356



362
535



363
206



364
186



365
649



366
301



370
800



371
360



372
227



373
588



374
417



375
159



376
645



377
404



378
594



379
309



380
214



381
539



382
449



383
331



384
609



385
119



386
771



387
217



388
188



389
551



390
229



391
568



392
333



393
408



394
650



395
310



396
596



397
339



398
420



399
541



400
218



401
657



402
368



403
773



404
123



405
230



406
555



407
175



408
832



409
391



410
313



411
610



412
241



413
652



414
450



415
334



416
777



417
220



418
542



419
341



420
600



421
424



422
314



423
658



424
183



428
355



429
673



430
125



431
287



432
583



433
395



434
557



435
234



436
785



437
316



438
345



439
563



440
187



441
660



442
452



443
778



444
403



445
558



446
342



447
397



448
587



449
207



450
616



451
236



452
676



453
432



454
705



455
346



456
565



457
361



458
674



459
126



463
780



464
405



465
589



466
215



467
664



468
398



469
566



470
303



471
597



472
358



473
801



474
419



475
624



476
456



477
786



478
348



479
189



480
569



481
244



482
590



483
410



484
647



485
219



486
706



487
311



488
595



489
362



490
802



491
464



492
680



493
406



494
788



498
570



499
248



500
651



501
369



502
834



503
190



504
708



505
409



506
613



507
315



508
572



509
364



510
659



511
422



512
335



513
221



514
688



515
451



516
792



517
370



518
611



519
425



520
601



521
235



522
804



523
343



524
653



525
412



526
833



527
480



528
712



529
222



530
602



531
317



532
543



533
453



534
654



535
426



536
614



537
372



538
775



539
433



540
559



541
237



542
898



543
617



544
347



545
808



546
243



547
720



548
454



549
665



550
318



551
604



552
376



556
238



557
675



558
359



559
836



560
458



561
625



562
399



563
662



564
677



565
245



566
567



567
434



568
816



569
457



570
618



571
349



572
787



573
465



574
781



575
897



576
363



577
666



578
407



579
591



580
127



581
620



582
246



583
736



584
436



585
678



586
571



587
350



591
460



592
707



593
840



594
411



595
782



596
365



597
789



598
440



599
599



600
374



601
668



602
628



603
423



604
900



605
466



606
848



607
803



608
250



609
790



610
371



611
709



612
191



613
573



614
689



615
481



616
682



617
413



618
603



619
793



620
366



621
713



622
468



626
655



627
252



628
806



629
414



630
684



631
904



632
373



633
615



634
482



635
632



636
805



637
223



638
794



639
864



640
427



641
690



642
472



643
714



644
835



645
455



646
809



647
377



648
605



649
619



650
435



651
663



652
721



653
319



654
796



655
430



656
692



657
912



658
239



659
606



660
716



661
461



662
810



663
484



664
838



665
667



666
378



667
817



668
621



669
437



670
837



671
722



672
247



673
696



674
380



675
737



676
679



677
459



678
812



679
627



680
488



684
622



685
928



686
351



687
724



688
783



689
469



690
629



691
818



692
438



693
669



694
462



695
738



696
683



697
251



698
842



699
849



700
496



701
901



702
820



703
728



704
467



705
633



706
902



707
367



708
670



709
791



710
442



711
844



712
630



713
474



714
685



715
850



719
379



720
865



721
795



722
415



723
824



724
960



725
740



726
253



727
905



728
634



729
444



730
693



731
744



732
485



733
807



734
686



735
906



736
470



737
575



738
715



739
375



740
866



741
913



742
473



743
852



744
636



745
797



746
431



747
694



748
811



749
486



750
752



754
856



755
908



756
254



757
717



758
607



759
930



760
476



761
697



762
725



763
914



764
439



765
819



766
839



767
868



768
492



769
718



770
698



771
381



772
813



773
623



774
814



775
498



776
872



777
739



778
929



779
445



780
671



781
916



782
821



783
463



784
726



785
961



786
843



787
490



788
631



789
729



790
700



791
382



792
741



793
845



794
920



795
471



796
822



797
851



798
932



799
730



800
497



801
880



802
635



803
742



804
443



805
687



806
903



807
825



808
475



812
732



813
500



814
853



815
936



816
826



817
446



818
695



819
745



820
867



821
637



822
487



823
799



824
907



825
746



826
828



827
493



828
857



829
699



830
964



831
915



832
477



833
854



834
909



835
719



836
504



837
748



838
944



839
858



840
873



841
638



842
478



843
754



847
499



848
910



849
815



850
870



851
931



852
255



853
968



854
860



855
701



856
756



857
922



858
491



859
731



860
823



861
874



862
976



863
918



864
502



865
933



866
743



867
760



868
881



869
494



870
702



871
921



872
827



873
876



874
934



875
847



876
505



877
733



878
963



882
383



883
855



884
924



885
992



886
734



887
829



888
965



889
501



890
938



891
884



892
945



893
749



894
859



895
755



896
479



897
966



898
830



899
888



900
940



901
750



902
871



903
506



904
970



905
911



906
757



907
946



908
969



909
861



910
977



911
447



912
875



913
919



914
639



915
758



916
948



917
862



918
761



919
508



920
972



921
923



922
877



923
952



924
886



925
935



926
978



927
762



928
503



929
883



930
703



931
993



932
925



933
878



934
980



935
941



936
764



940
994



941
735



942
939



943
984



944
967



945
889



946
947



947
831



948
507



949
942



950
751



951
973



952
996



953
890



954
949



955
759



956
892



957
971



958
1000



959
953



960
509



961
863



962
981



963
950



964
974



965
763



966
1008



967
979



968
879



969
954



970
986



971
995



975
765



976
956



977
997



978
982



979
887



980
985



981
943



982
998



983
1001



984
766



985
988



986
951



987
1004



988
893



989
1010



990
957



991
975



992
511



993
1002



994
894



995
983



996
1009



997
955



998
987



999
1012



1000
958



1001
999



1002
1005



1003
989



1004
1016



1005
990



1006
1011



1010
1006



1011
1017



1012
895



1013
1013



1014
991



1015
1018



1016
959



1017
1020



1018
1015



1019
1007



1020
1019



1021
1021



1022
1022



1023
1023










Sequence Q27, having a sequence length of 512:

    • [0, 1, 4, 8, 2, 16, 32, 6, 64, 3, 12, 5, 18, 128, 9, 33, 17, 10, 36, 66, 24, 256, 20, 65, 34, 7, 129, 40, 11, 72, 132, 19, 48, 68, 13, 257, 14, 21, 130, 26, 80, 35, 258, 38, 136, 96, 22, 37, 25, 67, 264, 41, 144, 28, 69, 260, 49, 74, 160, 42, 134, 70, 44, 81, 272, 15, 50, 131, 192, 73, 23, 137, 52, 288, 76, 133, 82, 27, 97, 259, 39, 56, 138, 84, 29, 145, 261, 43, 320, 98, 140, 265, 30, 88, 146, 262, 100, 161, 71, 45, 273, 51, 148, 266, 46, 75, 104, 164, 193, 53, 162, 384, 268, 77, 152, 54, 85, 289, 112, 274, 57, 78, 135, 194, 83, 290, 168, 276, 86, 58, 139, 322, 196, 101, 60, 147, 176, 280, 99, 89, 292, 141, 321, 200, 90, 31, 142, 102, 263, 47, 386, 105, 296, 208, 153, 92, 149, 267, 163, 324, 113, 150, 165, 55, 304, 106, 275, 269, 385, 154, 79, 108, 224, 166, 59, 169, 114, 195, 328, 270, 277, 87, 156, 116, 388, 336, 291, 278, 197, 61, 177, 170, 91, 281, 201, 198, 62, 143, 294, 172, 392, 103, 120, 293, 282, 352, 178, 202, 323, 297, 93, 107, 151, 209, 284, 180, 400, 94, 204, 298, 326, 155, 305, 109, 325, 210, 184, 225, 167, 300, 115, 387, 329, 110, 416, 212, 271, 117, 306, 157, 226, 171, 330, 337, 389, 308, 216, 121, 390, 158, 279, 332, 118, 173, 338, 179, 199, 353, 283, 312, 448, 228, 393, 122, 181, 232, 295, 174, 394, 63, 203, 354, 401, 340, 124, 285, 182, 299, 240, 211, 286, 344, 396, 205, 95, 418, 185, 213, 402, 307, 327, 356, 206, 186, 301, 111, 302, 360, 227, 417, 159, 404, 309, 214, 449, 331, 119, 217, 188, 229, 333, 408, 310, 339, 420, 218, 368, 123, 230, 175, 391, 313, 241, 450, 334, 220, 341, 424, 314, 183, 233, 355, 125, 287, 395, 234, 316, 345, 187, 452, 403, 342, 397, 207, 236, 432, 346, 361, 126, 242, 357, 405, 215, 398, 303, 358, 419, 456, 348, 189, 244, 410, 219, 311, 362, 464, 406, 421, 231, 248, 369, 190, 409, 315, 364, 422, 335, 221, 451, 370, 425, 235, 343, 412, 480, 222, 317, 453, 426, 372, 433, 237, 347, 243, 454, 318, 376, 428, 238, 359, 458, 399, 245, 434, 457, 349, 465, 363, 407, 127, 246, 436, 350, 249, 460, 411, 365, 440, 374, 423, 466, 250, 371, 191, 481, 413, 366, 468, 429, 252, 414, 373, 482, 223, 427, 472, 455, 377, 435, 319, 430, 239, 461, 484, 378, 437, 247, 380, 459, 488, 441, 351, 469, 438, 462, 251, 496, 467, 367, 442, 474, 483, 379, 415, 253, 444, 485, 470, 375, 473, 431, 486, 489, 254, 476, 439, 492, 381, 498, 445, 463, 490, 382, 471, 497, 443, 475, 500, 446, 487, 493, 477, 504, 478, 499, 255, 491, 502, 494, 505, 383, 501, 479, 506, 447, 508, 503, 495, 507, 509, 510, 511]









TABLE Q27







having a sequence length of 512:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
4



3
8



4
2



5
16



6
32



7
6



8
64



9
3



10
12



11
5



12
18



13
128



14
9



15
33



16
17



17
10



18
36



19
66



20
24



21
256



22
20



23
65



24
34



25
7



26
129



27
40



28
11



29
72



30
132



31
19



32
48



33
68



34
13



35
257



36
14



37
21



38
130



39
26



40
80



41
35



42
258



43
38



44
136



45
96



46
22



47
37



48
25



49
67



50
264



51
41



52
144



56
49



57
74



58
160



59
42



60
134



61
70



62
44



63
81



64
272



65
15



66
50



67
131



68
192



69
73



70
23



71
137



72
52



73
288



74
76



75
133



76
82



77
27



78
97



79
259



80
39



81
56



82
138



83
84



84
29



85
145



86
261



87
43



88
320



89
98



90
140



91
265



92
30



93
88



94
146



95
262



96
100



97
161



98
71



99
45



100
273



101
51



102
148



103
266



104
46



105
75



106
104



107
164



108
193



109
53



110
162



111
384



112
268



113
77



114
152



115
54



116
85



120
57



121
78



122
135



123
194



124
83



125
290



126
168



127
276



128
86



129
58



130
139



131
322



132
196



133
101



134
60



135
147



136
176



137
280



138
99



139
89



140
292



141
141



142
321



143
200



144
90



145
31



146
142



147
102



148
263



149
47



150
386



151
105



152
296



153
208



154
153



155
92



156
149



157
267



158
163



159
324



160
113



161
150



162
165



163
55



164
304



165
106



166
275



167
269



168
385



169
154



170
79



171
108



172
224



173
166



174
59



175
169



176
114



177
195



178
328



179
270



180
277



184
388



185
336



186
291



187
278



188
197



189
61



190
177



191
170



192
91



193
281



194
201



195
198



196
62



197
143



198
294



199
172



200
392



201
103



202
120



203
293



204
282



205
352



206
178



207
202



208
323



209
297



210
93



211
107



212
151



213
209



214
284



215
180



216
400



217
94



218
204



219
298



220
326



221
155



222
305



223
109



224
325



225
210



226
184



227
225



228
167



229
300



230
115



231
387



232
329



233
110



234
416



235
212



236
271



237
117



238
306



239
157



240
226



241
171



242
330



243
337



244
389



248
390



249
158



250
279



251
332



252
118



253
173



254
338



255
179



256
199



257
353



258
283



259
312



260
448



261
228



262
393



263
122



264
181



265
232



266
295



267
174



268
394



269
63



270
203



271
354



272
401



273
340



274
124



275
285



276
182



277
299



278
240



279
211



280
286



281
344



282
396



283
205



284
95



285
418



286
185



287
213



288
402



289
307



290
327



291
356



292
206



293
186



294
301



295
111



296
302



297
360



298
227



299
417



300
159



301
404



302
309



303
214



304
449



305
331



306
119



307
217



308
188



312
310



313
339



314
420



315
218



316
368



317
123



318
230



319
175



320
391



321
313



322
241



323
450



324
334



325
220



326
341



327
424



328
314



329
183



330
233



331
355



332
125



333
287



334
395



335
234



336
316



337
345



338
187



339
452



340
403



341
342



342
397



343
207



344
236



345
432



346
346



347
361



348
126



349
242



350
357



351
405



352
215



353
398



354
303



355
358



356
419



357
456



358
348



359
189



360
244



361
410



362
219



363
311



364
362



365
464



366
406



367
421



368
231



369
248



370
369



371
190



372
409



376
335



377
221



378
451



379
370



380
425



381
235



382
343



383
412



384
480



385
222



386
317



387
453



388
426



389
372



390
433



391
237



392
347



393
243



394
454



395
318



396
376



397
428



398
238



399
359



400
458



401
399



402
245



403
434



404
457



405
349



406
465



407
363



408
407



409
127



410
246



411
436



412
350



413
249



414
460



415
411



416
365



417
440



418
374



419
423



420
466



421
250



422
371



423
191



424
481



425
413



426
366



427
468



428
429



429
252



430
414



431
373



432
482



433
223



434
427



435
472



436
455



440
430



441
239



442
461



443
484



444
378



445
437



446
247



447
380



448
459



449
488



450
441



451
351



452
469



453
438



454
462



455
251



456
496



457
467



458
367



459
442



460
474



461
483



462
379



463
415



464
253



465
444



466
485



467
470



468
375



469
473



470
431



471
486



472
489



473
254



474
476



475
439



476
492



477
381



478
498



479
445



480
463



481
490



482
382



483
471



484
497



485
443



486
475



487
500



488
446



489
487



490
493



491
477



492
504



493
478



494
499



495
255



496
491



497
502



498
494



499
505



500
383



504
447



505
508



506
503



507
495



508
507



509
509



510
510



511
511










Sequence Q28, having a sequence length of 256:

    • [0, 1, 4, 8, 2, 16, 32, 6, 64, 3, 12, 5, 18, 128, 9, 33, 17, 10, 36, 66, 24, 20, 65, 34, 7, 129, 40, 11, 72, 132, 19, 48, 68, 13, 14, 21, 130, 26, 80, 35, 38, 136, 96, 22, 37, 25, 67, 41, 144, 28, 69, 49, 74, 160, 42, 134, 70, 44, 81, 15, 50, 131, 192, 73, 23, 137, 52, 76, 133, 82, 27, 97, 39, 56, 138, 84, 29, 145, 43, 98, 140, 30, 88, 146, 100, 161, 71, 45, 51, 148, 46, 75, 104, 164, 193, 53, 162, 77, 152, 54, 85, 112, 57, 78, 135, 194, 83, 168, 86, 58, 139, 196, 101, 60, 147, 176, 99, 89, 141, 200, 90, 31, 142, 102, 47, 105, 208, 153, 92, 149, 163, 113, 150, 165, 55, 106, 154, 79, 108, 224, 166, 59, 169, 114, 195, 87, 156, 116, 197, 61, 177, 170, 91, 201, 198, 62, 143, 172, 103, 120, 178, 202, 93, 107, 151, 209, 180, 94, 204, 155, 109, 210, 184, 225, 167, 115, 110, 212, 117, 157, 226, 171, 216, 121, 158, 118, 173, 179, 199, 228, 122, 181, 232, 174, 63, 203, 124, 182, 240, 211, 205, 95, 185, 213, 206, 186, 111, 227, 159, 214, 119, 217, 188, 229, 218, 123, 230, 175, 241, 220, 183, 233, 125, 234, 187, 207, 236, 126, 242, 215, 189, 244, 219, 231, 248, 190, 221, 235, 222, 237, 243, 238, 245, 127, 246, 249, 250, 191, 252, 223, 239, 247, 251, 253, 254, 255]









TABLE Q28







having a sequence length of 256:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
4



3
8



4
2



5
16



6
32



7
6



8
64



9
3



10
12



11
5



12
18



13
128



14
9



15
33



16
17



17
10



18
36



19
66



20
24



21
20



22
65



23
34



24
7



25
129



26
40



27
11



28
72



29
132



30
19



31
48



32
68



33
13



34
14



35
21



36
130



37
26



38
80



39
35



40
38



41
136



42
96



43
22



44
37



45
25



46
67



47
41



48
144



49
28



50
69



51
49



52
74



53
160



54
42



55
134



56
70



57
44



58
81



59
15



60
50



61
131



62
192



63
73



64
23



65
137



66
52



67
76



68
133



69
82



70
27



71
97



72
39



73
56



74
138



75
84



76
29



77
145



78
43



79
98



80
140



81
30



82
88



83
146



84
100



85
161



86
71



87
45



88
51



89
148



90
46



91
75



92
104



93
164



94
193



95
53



96
162



97
77



98
152



99
54



100
185



101
112



102
57



103
78



104
135



105
194



106
83



107
168



108
86



109
58



110
139



111
196



112
101



113
60



114
147



115
176



116
99



117
89



118
141



119
200



120
90



121
31



122
142



123
102



124
47



125
105



126
208



127
153



128
92



129
149



130
163



131
113



132
150



133
165



134
55



135
106



136
154



137
79



138
108



139
224



140
166



141
59



142
169



143
114



144
195



145
87



146
156



147
116



148
197



149
61



150
177



151
170



152
91



153
201



154
198



155
62



156
143



157
172



158
103



159
120



160
178



161
202



162
93



163
107



164
151



165
209



166
180



167
94



168
204



169
155



170
109



171
210



172
184



173
225



174
167



175
115



176
110



177
212



178
117



179
157



180
226



181
171



182
216



183
121



184
158



185
118



186
173



187
179



188
199



189
228



190
122



191
181



192
232



193
174



194
63



195
203



196
124



197
182



198
240



199
211



200
205



201
95



202
185



203
213



204
206



205
186



206
111



207
227



208
159



209
214



210
119



211
217



212
188



213
229



214
218



215
123



216
230



217
175



218
241



219
220



220
183



221
233



222
125



223
234



224
187



225
207



226
236



227
126



228
242



229
215



230
189



231
244



232
219



233
231



234
248



235
190



236
221



237
235



238
222



239
237



240
243



241
238



242
245



243
127



244
246



245
249



246
250



247
191



248
252



249
223



250
239



251
247



252
251



253
253



254
254



255
255










Sequence Q29, having a sequence length of 128:

    • [0, 1, 4, 8, 2, 16, 32, 6, 64, 3, 12, 5, 18, 9, 33, 17, 10, 36, 66, 24, 20, 65, 34, 7, 40, 11, 72, 19, 48, 68, 13, 14, 21, 26, 80, 35, 38, 96, 22, 37, 25, 67, 41, 28, 69, 49, 74, 42, 70, 44, 81, 15, 50, 73, 23, 52, 76, 82, 27, 97, 39, 56, 84, 29, 43, 98, 30, 88, 100, 71, 45, 51, 46, 75, 104, 53, 77, 54, 85, 112, 57, 78, 83, 86, 58, 101, 60, 99, 89, 90, 31, 102, 47, 105, 92, 113, 55, 106, 79, 108, 59, 114, 87, 116, 61, 91, 62, 103, 120, 93, 107, 94, 109, 115, 110, 117, 121, 118, 122, 63, 124, 95, 111, 119, 123, 125, 126, 127]












TABLE Q29, having a sequence length of 128:










Reliability or sequence
Polarized channel



number of reliability
sequence number














0
0



1
1



2
4



3
8



4
2



5
16



6
32



7
6



8
64



9
3



10
12



11
5



12
18



13
9



14
33



15
17



16
10



17
36



18
66



19
24



20
20



21
65



22
34



23
7



24
40



25
11



26
72



27
19



28
48



29
68



30
13



31
14



32
21



33
26



34
80



35
35



36
38



37
96



38
22



39
37



40
25



41
67



42
41



43
28



44
69



45
49



46
74



47
42



48
70



49
44



50
81



51
15



52
50



53
73



54
23



55
52



56
76



57
82



58
27



59
97



60
39



61
56



62
84



63
29



64
43



65
98



66
30



67
88



68
100



69
71



70
45



71
51



72
46



73
75



74
104



75
53



76
77



77
54



78
85



79
112



80
57



81
78



82
83



83
86



84
58



85
101



86
60



87
99



88
89



89
90



90
31



91
102



92
47



93
105



94
92



95
113



96
55



97
106



98
79



99
108



100
59



101
114



102
87



103
116



104
61



105
91



106
62



107
103



108
120



109
93



110
107



111
94



112
109



113
115



114
110



115
117



116
121



117
118



118
122



119
63



120
124



121
95



122
111



123
119



124
123



125
125



126
126



127
127










Sequence Q30, having a sequence length of 64:

    • [0, 1, 4, 8, 2, 16, 32, 6, 3, 12, 5, 18, 9, 33, 17, 10, 36, 24, 20, 34, 7, 40, 11, 19, 48, 13, 14, 21, 26, 35, 38, 22, 37, 25, 41, 28, 49, 42, 44, 15, 50, 23, 52, 27, 39, 56, 29, 43, 30, 45, 51, 46, 53, 54, 57, 58, 60, 31, 47, 55, 59, 61, 62, 63]









TABLE Q30





having a sequence length of 64:






















Reliability
Polarized
Reliability
Polarized
Reliability
Polarized
Reliability
Polarized


or sequence
channel
or sequence
channel
or sequence
channel
or sequence
channel


number of
sequence
number of
sequence
number of
sequence
number of
sequence


reliability
number
reliability
number
reliability
number
reliability
number





0
0
8
3
16
36
24
48


1
1
9
12
17
24
25
13


2
4
10
5
18
20
26
14


3
8
11
18
19
34
27
21


4
2
12
9
20
7
28
26


5
16
13
33
21
40
29
35


6
32
14
17
22
11
30
38


7
6
15
10
23
19
31
22





Reliability
Polarized
Reliability
Polarized
Reliability
Polarized
Reliability
Polarized


or sequence
channel
or sequence
channel
or sequence
channel
or sequence
channel


number of
sequence
number of
sequence
number of
sequence
number of
sequence


reliability
number
reliability
number
reliability
number
reliability
number





32
37
40
50
48
30
56
60


33
25
41
23
49
45
57
31


34
41
42
52
50
51
58
47


35
28
43
27
51
46
59
55


36
49
44
39
52
53
60
59


37
42
45
56
53
54
61
61


38
44
46
29
54
57
62
62


39
15
47
43
55
58
63
63









Sequence Z26, having a sequence length of 1024:

    • [0, 1, 4, 10, 2, 12, 7, 26, 3, 15, 18, 29, 11, 36, 38, 69, 5, 17, 13, 33, 23, 39, 48, 74, 21, 51, 41, 82, 56, 90, 99, 161, 6, 16, 25, 43, 19, 50, 45, 85, 28, 54, 62, 93, 66, 107, 113, 166, 34, 59, 70, 109, 77, 118, 125, 183, 87, 131, 142, 197, 148, 216, 225, 327, 8, 24, 20, 52, 35, 57, 65, 106, 30, 73, 60, 114, 79, 123, 132, 192, 42, 67, 81, 136, 89, 126, 140, 205, 100, 153, 159, 220, 173, 243, 253, 350, 47, 83, 96, 152, 103, 146, 163, 231, 115, 168, 185, 245, 193, 261, 275, 367, 129, 179, 199, 271, 208, 280, 302, 385, 233, 295, 318, 404, 335, 430, 459, 580, 14, 27, 40, 71, 31, 80, 64, 133, 46, 76, 88, 143, 97, 156, 162, 226, 55, 91, 101, 149, 110, 174, 180, 246, 124, 172, 190, 258, 207, 283, 298, 375, 61, 105, 119, 177, 116, 182, 195, 268, 138, 198, 218, 286, 229, 303, 324, 407, 150, 217, 238, 306, 250, 319, 338, 424, 265, 353, 364, 440, 388, 479, 503, 612, 72, 117, 135, 200, 145, 214, 223, 308, 158, 222, 239, 328, 254, 348, 363, 449, 170, 247, 264, 342, 278, 355, 380, 466, 293, 387, 400, 485, 417, 513, 529, 637, 194, 266, 285, 372, 315, 390, 405, 497, 321, 426, 435, 521, 451, 541, 556, 658, 341, 412, 460, 546, 481, 565, 582, 672, 499, 589, 608, 697, 627, 726, 756, 852, 22, 37, 44, 84, 58, 92, 102, 164, 53, 98, 111, 175, 122, 188, 203, 279, 68, 108, 130, 186, 139, 204, 213, 299, 151, 221, 235, 311, 249, 336, 344, 431, 78, 128, 137, 212, 155, 234, 227, 322, 169, 242, 255, 339, 269, 366, 369, 470, 184, 260, 282, 358, 292, 379, 395, 487, 312, 410, 422, 507, 437, 531, 550, 653, 94, 157, 144, 241, 178, 262, 257, 359, 202, 273, 287, 383, 300, 392, 415, 512, 211, 289, 305, 397, 333, 419, 446, 523, 345, 438, 455, 544, 478, 571, 587, 686, 237, 309, 330, 428, 361, 462, 472, 558, 371, 457, 489, 576, 509, 596, 620, 707, 402, 501, 517, 610, 537, 632, 600, 739, 552, 647, 666, 719, 674, 771, 791, 882, 121, 189, 167, 272, 209, 290, 296, 409, 230, 317, 325, 433, 347, 447, 468, 562, 251, 332, 356, 444, 377, 464, 493, 578, 393, 505, 483, 594, 525, 617, 629, 722, 276, 374, 351, 474, 398, 495, 511, 603, 421, 519, 535, 640, 554, 624, 655, 746, 453, 539, 567, 650, 584, 669, 692, 764, 598, 683, 710, 804, 729, 779, 817, 911, 314, 382, 414, 515, 442, 533, 548, 645, 476, 569, 560, 677, 591, 661, 694, 783, 491, 573, 605, 704, 622, 689, 736, 795, 642, 742, 713, 808, 760, 832, 842, 896, 527, 615, 634, 716, 663, 732, 749, 822, 680, 753, 787, 858, 768, 827, 869, 937, 700, 800, 775, 847, 813, 889, 864, 928, 836, 876, 903, 948, 919, 960, 974, 992, 9, 32, 75, 120, 49, 134, 104, 210, 63, 154, 171, 224, 127, 248, 256, 349, 86, 165, 141, 236, 196, 259, 291, 362, 187, 297, 267, 381, 313, 399, 418, 532, 95, 160, 206, 274, 176, 294, 281, 389, 219, 307, 331, 406, 340, 434, 445, 540, 240, 323, 352, 439, 368, 456, 469, 566, 391, 480, 498, 586, 508, 613, 625, 737, 112, 201, 181, 301, 244, 316, 337, 432, 228, 360, 326, 448, 373, 465, 482, 579, 270, 343, 378, 488, 396, 471, 496, 599, 420, 520, 530, 618, 551, 648, 659, 758, 288, 384, 411, 518, 427, 506, 536, 633, 450, 543, 570, 649, 581, 668, 684, 773, 475, 561, 590, 679, 602, 690, 712, 788, 635, 705, 728, 802, 744, 821, 841, 914, 147, 215, 263, 354, 232, 376, 334, 484, 284, 365, 394, 500, 413, 524, 534, 626, 310, 401, 423, 510, 441, 553, 563, 651, 467, 549, 577, 665, 601, 693, 708, 780, 329, 429, 458, 557, 452, 564, 585, 676, 492, 588, 616, 696, 630, 714, 734, 805, 514, 614, 641, 717, 656, 730, 747, 818, 673, 761, 770, 829, 790, 855, 870, 930, 357, 454, 486, 592, 504, 611, 623, 718, 528, 621, 643, 738, 660, 757, 769, 835, 547, 652, 671, 751, 687, 762, 784, 846, 703, 789, 799, 859, 812, 877, 886, 941, 583, 675, 695, 777, 725, 792, 803, 866, 731, 819, 825, 881, 837, 893, 901, 950, 750, 809, 843, 895, 856, 906, 915, 955, 867, 918, 927, 965, 936, 975, 984, 1007, 191, 252, 277, 386, 320, 403, 425, 538, 304, 416, 443, 555, 463, 574, 595, 688, 346, 436, 477, 572, 494, 597, 609, 709, 516, 619, 638, 721, 654, 745, 752, 823, 370, 473, 490, 607, 522, 636, 628, 733, 545, 646, 662, 748, 678, 772, 774, 849, 568, 667, 691, 765, 702, 782, 796, 860, 723, 807, 816, 872, 826, 887, 898, 947, 408, 526, 502, 644, 559, 670, 664, 766, 593, 682, 698, 786, 711, 793, 811, 875, 606, 699, 715, 797, 743, 814, 833, 883, 754, 828, 839, 894, 854, 909, 917, 961, 639, 720, 740, 820, 767, 844, 850, 902, 776, 840, 861, 912, 873, 922, 933, 968, 801, 868, 879, 929, 891, 939, 924, 979, 899, 945, 953, 972, 956, 988, 994, 1012, 461, 575, 542, 681, 604, 701, 706, 806, 631, 727, 735, 824, 755, 834, 848, 905, 657, 741, 763, 831, 781, 845, 863, 913, 794, 871, 857, 921, 884, 932, 938, 973, 685, 778, 759, 851, 798, 865, 874, 925, 815, 880, 890, 942, 900, 935, 949, 981, 838, 892, 907, 946, 916, 954, 963, 986, 923, 959, 969, 997, 976, 990, 1000, 1016, 724, 785, 810, 878, 830, 888, 897, 944, 853, 908, 904, 957, 920, 951, 964, 991, 862, 910, 926, 967, 934, 962, 978, 995, 943, 980, 970, 998, 985, 1003, 1005, 1014, 885, 931, 940, 971, 952, 977, 982, 1001, 958, 983, 993, 1008, 987, 1002, 1010, 1019, 966, 996, 989, 1006, 999, 1013, 1009, 1018, 1004, 1011, 1015, 1020, 1017, 1021, 1022, 1023]












Table Z26, having a sequence length of 1024:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
4



3
10



4
2



5
12



6
7



7
26



8
3



9
15



10
18



11
29



12
11



13
36



14
38



15
69



16
5



17
17



18
13



19
33



20
23



21
39



22
48



23
74



24
21



25
51



26
41



27
82



28
56



29
90



30
99



31
161



32
6



33
16



34
25



35
43



36
19



37
50



38
45



39
85



40
28



41
54



42
62



43
93



44
66



45
107



46
113



47
166



48
34



49
59



50
70



51
109



52
77



53
118



54
125



55
183



56
87



57
131



58
142



59
197



60
148



61
216



62
225



63
327



64
8



65
24



66
20



67
52



68
35



69
57



70
65



71
106



72
30



73
73



74
60



75
114



76
79



77
123



78
132



79
192



80
42



81
67



82
81



83
136



84
89



85
126



86
140



87
205



88
100



89
153



90
159



91
220



92
173



93
243



94
253



95
350



96
47



97
83



98
96



99
152



100
103



101
146



102
163



103
231



104
115



105
168



106
185



107
245



108
193



109
261



110
275



111
367



112
129



113
179



114
199



115
271



116
208



117
280



118
302



119
385



120
233



121
295



122
318



123
404



124
335



125
430



126
459



127
580



128
14



129
27



130
40



131
71



132
31



133
80



134
64



135
133



136
46



137
76



138
88



139
143



140
97



141
156



142
162



143
226



144
55



145
91



146
101



147
149



148
110



149
174



150
180



151
246



152
124



153
172



154
190



155
258



156
207



157
283



158
298



159
375



160
61



161
105



162
119



163
177



164
116



165
182



166
195



167
268



168
138



169
198



170
218



171
286



172
229



173
303



174
324



175
407



176
150



177
217



178
238



179
306



180
250



181
319



182
338



183
424



184
265



185
353



186
364



187
440



188
388



189
479



190
503



191
612



192
72



193
117



194
135



195
200



196
145



197
214



198
223



199
308



200
158



201
222



202
239



203
328



204
254



205
348



206
363



207
449



208
170



209
247



210
264



211
342



212
278



213
355



214
380



215
466



216
293



217
387



218
400



219
485



220
417



221
513



222
529



223
637



224
194



225
266



226
285



227
372



228
315



229
390



230
405



231
497



232
321



233
426



234
435



235
521



236
451



237
541



238
556



239
658



240
341



241
412



242
460



243
546



244
481



245
565



246
582



247
672



248
499



249
589



250
608



251
697



252
627



253
726



254
756



255
852



256
22



257
37



258
44



259
84



260
58



261
92



262
102



263
164



264
53



265
98



266
111



267
175



268
122



269
188



270
203



271
279



272
68



273
108



274
130



275
186



276
139



277
204



278
213



279
299



280
151



281
221



282
235



283
311



284
249



285
336



286
344



287
431



288
78



289
128



290
137



291
212



292
155



293
234



294
227



295
322



296
169



297
242



298
255



299
339



300
269



301
366



302
369



303
470



304
184



305
260



306
282



307
358



308
292



309
379



310
395



311
487



312
312



313
410



314
422



315
507



316
437



317
531



318
550



319
653



320
94



321
157



322
144



323
241



324
178



325
262



326
257



327
359



328
202



329
273



330
287



331
383



332
300



333
392



334
415



335
512



336
211



337
289



338
305



339
397



340
333



341
419



342
446



343
523



344
345



345
438



346
455



347
544



348
478



349
571



350
587



351
686



352
237



353
309



354
330



355
428



356
361



357
462



358
472



359
558



360
371



361
457



362
489



363
576



364
509



365
596



366
620



367
707



368
402



369
501



370
517



371
610



372
537



373
632



374
600



375
739



376
552



377
647



378
666



379
719



380
674



381
771



382
791



383
882



384
121



385
189



386
167



387
272



388
209



389
290



390
296



391
409



392
230



393
317



394
325



395
433



396
347



397
447



398
468



399
562



400
251



401
332



402
356



403
444



404
377



405
464



406
493



407
578



408
393



409
505



410
483



411
594



412
525



413
617



414
629



415
722



416
276



417
374



418
351



419
474



420
398



421
495



422
511



423
603



424
421



425
519



426
535



427
640



428
554



429
624



430
655



431
746



432
453



433
539



434
567



435
650



436
584



437
669



438
692



439
764



440
598



441
683



442
710



443
804



444
729



445
779



446
817



447
911



448
314



449
382



450
414



451
515



452
442



453
533



454
548



455
645



456
476



457
569



458
560



459
677



460
591



461
661



462
694



463
783



464
491



465
573



466
605



467
704



468
622



469
689



470
736



471
795



472
642



473
742



474
713



475
808



476
760



477
832



478
842



479
896



480
527



481
615



482
634



483
716



484
663



485
732



486
749



487
822



488
680



489
753



490
787



491
858



492
768



493
827



494
869



495
937



496
700



497
800



498
775



499
847



500
813



501
889



502
864



503
928



504
836



505
876



506
903



507
948



508
919



509
960



510
974



511
992



512
9



513
32



514
75



515
120



516
49



517
134



518
104



519
210



520
63



521
154



522
171



523
224



524
127



525
248



526
256



527
349



528
86



529
165



530
141



531
236



532
196



533
259



534
291



535
362



536
187



537
297



538
267



539
381



540
313



541
399



542
418



543
532



544
95



545
160



546
206



547
274



548
176



549
294



550
281



551
389



552
219



553
307



554
331



555
406



556
340



557
434



558
445



559
540



560
240



561
323



562
352



563
439



564
368



565
456



566
469



567
566



568
391



569
480



570
498



571
586



572
508



573
613



574
625



575
737



576
112



577
201



578
181



579
301



580
244



581
316



582
337



583
432



584
228



585
360



586
326



587
448



588
373



589
465



590
482



591
579



592
270



593
343



594
378



595
488



596
396



597
471



598
496



599
599



600
420



601
520



602
530



603
618



604
551



605
648



606
659



607
758



608
288



609
384



610
411



611
518



612
427



613
506



614
536



615
633



616
450



617
543



618
570



619
649



620
581



621
668



622
684



623
773



624
475



625
561



626
590



627
679



628
602



629
690



630
712



631
788



632
635



633
705



634
728



635
802



636
744



637
821



638
841



639
914



640
147



641
215



642
263



643
354



644
232



645
376



646
334



647
484



648
284



649
365



650
394



651
500



652
413



653
524



654
534



655
626



656
310



657
401



658
423



659
510



660
441



661
553



662
563



663
651



664
467



665
549



666
577



667
665



668
601



669
693



670
708



671
780



672
329



673
429



674
458



675
557



676
452



677
564



678
585



679
676



680
492



381
588



682
616



683
696



684
630



685
714



686
734



687
805



688
514



689
614



690
641



691
717



692
656



693
730



694
747



695
818



696
673



697
761



698
770



699
829



700
790



701
855



702
870



703
930



704
357



705
454



706
486



707
592



708
504



709
611



710
623



711
718



712
528



713
621



714
643



715
738



716
660



717
757



718
769



719
835



720
547



721
652



722
671



723
751



724
687



725
762



726
784



727
846



728
703



729
789



730
799



731
859



732
812



733
877



734
886



735
941



736
583



737
675



738
695



739
777



740
725



741
792



742
803



743
866



744
731



745
819



746
825



747
881



748
837



749
893



750
901



751
950



752
750



753
809



754
843



755
895



756
856



757
906



758
915



759
955



760
867



761
918



762
927



763
965



764
936



765
975



766
984



767
1007



768
191



769
252



770
277



771
386



772
320



773
403



774
425



775
538



776
304



777
416



778
443



779
555



780
463



781
574



782
595



783
688



784
346



785
436



786
477



787
572



788
494



789
597



790
609



791
709



792
516



793
619



794
638



795
721



796
654



797
745



798
752



799
823



800
370



801
473



802
490



803
607



804
522



805
636



806
628



807
733



808
545



809
646



810
662



811
748



812
678



813
772



814
774



815
849



816
568



817
667



818
691



819
765



820
702



821
782



822
796



823
860



824
723



825
807



826
816



827
872



828
826



829
887



830
898



831
947



832
408



833
526



834
502



835
644



836
559



837
670



838
664



839
766



840
593



841
682



842
698



843
786



844
711



845
793



846
811



847
875



848
606



849
699



850
715



851
797



852
743



853
814



854
833



855
883



856
754



857
828



858
839



859
894



860
854



861
909



862
917



863
961



864
639



865
720



866
740



867
820



868
767



869
844



870
850



871
902



872
776



873
840



874
861



875
912



876
873



877
922



878
933



879
968



880
801



881
868



882
879



883
929



884
891



885
939



886
924



887
979



888
899



889
945



890
953



891
972



892
956



893
988



894
994



895
1012



896
461



897
575



898
542



899
681



900
604



901
701



902
706



903
806



904
631



905
727



906
735



907
824



908
755



909
834



910
848



911
905



912
657



913
741



914
763



915
831



916
781



917
845



918
863



919
913



920
794



921
871



922
857



923
921



924
884



925
932



926
938



927
973



928
685



929
778



930
759



931
851



932
798



933
865



934
874



935
925



936
815



937
880



938
890



939
942



940
900



941
935



942
949



943
981



944
838



945
892



946
907



947
946



948
916



949
954



950
963



951
986



952
923



953
959



954
969



955
997



956
976



957
990



958
1000



959
1016



960
724



961
785



962
810



963
878



964
830



965
888



966
897



967
944



968
853



969
908



970
904



971
957



972
920



973
951



974
964



975
991



976
862



977
910



978
926



979
967



980
934



981
962



982
978



983
995



984
943



985
980



986
970



987
998



988
985



989
1003



990
1005



991
1014



992
885



993
931



994
940



995
971



996
952



997
977



998
982



999
1001



1000
958



1001
983



1002
993



1003
1008



1004
987



1005
1002



1006
1010



1007
1019



1008
966



1009
996



1010
989



1011
1006



1012
999



1013
1013



1014
1009



1015
1018



1016
1004



1017
1011



1018
1015



1019
1020



1020
1017



1021
1021



1022
1022



1023
1023










Sequence Z27, having a sequence length of 512:

    • [0, 1, 4, 9, 2, 11, 7, 25, 3, 14, 17, 28, 10, 34, 36, 65, 5, 16, 12, 31, 22, 37, 46, 70, 20, 48, 39, 77, 53, 84, 92, 145, 6, 15, 24, 41, 18, 47, 43, 80, 27, 51, 59, 87, 62, 99, 104, 149, 32, 56, 66, 101, 72, 109, 115, 163, 81, 120, 129, 174, 134, 189, 196, 269, 8, 23, 19, 49, 33, 54, 61, 98, 29, 69, 57, 105, 74, 113, 121, 170, 40, 63, 76, 124, 83, 116, 128, 181, 93, 139, 144, 192, 155, 210, 217, 284, 45, 78, 89, 138, 96, 133, 147, 201, 106, 151, 165, 211, 171, 223, 233, 295, 118, 160, 176, 230, 183, 237, 252, 306, 202, 247, 263, 317, 274, 332, 348, 409, 13, 26, 38, 67, 30, 75, 60, 122, 44, 71, 82, 130, 90, 141, 146, 197, 52, 85, 94, 135, 102, 156, 161, 212, 114, 154, 169, 221, 182, 239, 249, 300, 58, 97, 110, 158, 107, 162, 173, 228, 126, 175, 191, 241, 199, 253, 267, 319, 136, 190, 206, 255, 215, 264, 276, 329, 226, 286, 293, 338, 308, 359, 371, 423, 68, 108, 123, 177, 132, 188, 195, 256, 143, 194, 207, 270, 218, 283, 292, 343, 153, 213, 225, 279, 235, 287, 303, 352, 246, 307, 315, 362, 325, 377, 385, 433, 172, 227, 240, 298, 261, 309, 318, 368, 265, 330, 335, 381, 344, 391, 398, 441, 278, 322, 349, 393, 360, 402, 410, 446, 369, 413, 421, 455, 429, 464, 473, 495, 21, 35, 42, 79, 55, 86, 95, 148, 50, 91, 103, 157, 112, 167, 179, 236, 64, 100, 119, 166, 127, 180, 187, 250, 137, 193, 204, 258, 214, 275, 280, 333, 73, 117, 125, 186, 140, 203, 198, 266, 152, 209, 219, 277, 229, 294, 296, 354, 164, 222, 238, 289, 245, 302, 312, 363, 259, 321, 328, 373, 336, 386, 395, 439, 88, 142, 131, 208, 159, 224, 220, 290, 178, 232, 242, 305, 251, 310, 324, 376, 185, 243, 254, 313, 273, 326, 341, 382, 281, 337, 346, 392, 358, 405, 412, 451, 205, 257, 271, 331, 291, 350, 355, 399, 297, 347, 364, 407, 374, 416, 426, 458, 316, 370, 379, 422, 389, 431, 418, 468, 396, 437, 444, 462, 447, 477, 482, 500, 111, 168, 150, 231, 184, 244, 248, 320, 200, 262, 268, 334, 282, 342, 353, 401, 216, 272, 288, 340, 301, 351, 366, 408, 311, 372, 361, 415, 383, 425, 430, 463, 234, 299, 285, 356, 314, 367, 375, 419, 327, 380, 388, 434, 397, 428, 440, 470, 345, 390, 403, 438, 411, 445, 453, 475, 417, 450, 459, 485, 465, 479, 488, 504, 260, 304, 323, 378, 339, 387, 394, 436, 357, 404, 400, 448, 414, 442, 454, 480, 365, 406, 420, 457, 427, 452, 467, 483, 435, 469, 460, 486, 474, 491, 493, 502, 384, 424, 432, 461, 443, 466, 471, 489, 449, 472, 481, 496, 476, 490, 498, 507, 456, 484, 478, 494, 487, 501, 497, 506, 492, 499, 503, 508, 505, 509, 510, 511]












TABLE Z27, having a sequence length of 512:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
4



3
9



4
2



5
11



6
7



7
25



8
3



9
14



10
17



11
28



12
10



13
34



14
36



15
65



16
5



17
16



18
12



19
31



20
22



21
37



22
46



23
70



24
20



25
48



26
39



27
77



28
53



29
84



30
92



31
145



32
6



33
15



34
24



35
41



36
18



37
47



38
43



39
80



40
27



41
51



42
59



43
87



44
62



45
99



46
104



47
149



48
32



49
56



50
66



51
101



52
72



53
109



54
115



55
163



56
81



57
120



58
129



59
174



60
134



61
189



62
196



63
269



64
8



65
23



66
19



67
49



68
33



69
54



70
61



71
98



72
29



73
69



74
57



75
105



76
74



77
113



78
121



79
170



80
40



81
63



82
76



83
124



84
83



85
116



86
128



87
181



88
93



89
139



90
144



91
192



92
155



93
210



94
217



95
284



96
45



97
78



98
89



99
138



100
96



101
133



102
147



103
201



104
106



105
151



106
165



107
211



108
171



109
223



110
233



111
295



112
118



113
160



114
176



115
230



116
183



117
237



118
252



119
306



120
202



121
247



122
263



123
317



124
274



125
332



126
348



127
409



128
13



129
26



130
38



131
67



132
30



133
75



134
60



135
122



136
44



137
71



138
82



139
130



140
90



141
141



142
146



143
197



144
52



145
85



146
94



147
135



148
102



149
156



150
161



151
212



152
114



153
154



154
169



155
221



156
182



157
239



158
249



159
300



160
58



161
97



162
110



163
158



164
107



165
162



166
173



167
228



168
126



169
175



170
191



171
241



172
199



173
253



174
267



175
319



176
136



177
190



178
206



179
255



180
215



181
264



182
276



183
329



184
226



185
286



186
293



187
338



188
308



189
359



190
371



191
423



192
68



193
108



194
123



195
177



196
132



197
188



198
195



199
256



200
143



201
194



202
207



203
270



204
218



205
283



206
292



207
343



208
153



209
213



210
225



211
279



212
235



213
287



214
303



215
352



216
246



217
307



218
315



219
362



220
325



221
377



222
385



223
433



224
172



225
227



226
240



227
298



228
261



229
309



230
318



231
368



232
265



233
330



234
335



235
381



236
344



237
391



238
398



239
441



240
278



241
322



242
349



243
393



244
360



245
402



246
410



247
446



248
369



249
413



250
421



251
455



252
429



253
464



254
473



255
495



256
21



257
35



258
42



259
79



260
55



261
86



262
95



263
148



264
50



265
91



266
103



267
157



268
112



269
167



270
179



271
236



272
64



273
100



274
119



275
166



276
127



277
180



278
187



279
250



280
137



281
193



282
204



283
258



284
214



285
275



286
280



287
333



288
73



289
117



290
125



291
186



292
140



293
203



294
198



295
266



296
152



297
209



298
219



299
277



300
229



301
294



302
296



303
354



304
164



305
222



306
238



307
289



308
245



309
302



310
312



311
363



312
259



313
321



314
328



315
373



316
336



317
386



318
395



319
439



320
88



321
142



322
131



323
208



324
159



325
224



326
220



327
290



328
178



329
232



330
242



331
305



332
251



333
310



334
324



335
376



336
185



337
243



338
254



339
313



340
273



341
326



342
341



343
382



344
281



345
337



346
346



347
392



348
358



349
405



350
412



351
451



352
205



353
257



354
271



355
331



356
291



357
350



358
355



359
399



360
297



361
347



362
364



363
407



364
374



365
416



366
426



367
458



368
316



369
370



370
379



371
422



372
389



373
431



374
418



375
468



376
396



377
437



378
444



379
462



380
447



381
477



382
482



383
500



384
111



385
168



386
150



387
231



388
184



389
244



390
248



391
320



392
200



393
262



394
268



395
334



396
282



397
342



398
353



399
401



400
216



401
272



402
288



403
340



404
301



405
351



406
366



407
408



408
311



409
372



410
361



411
415



412
383



413
425



414
430



415
463



416
234



417
299



418
285



419
356



420
314



421
367



422
375



423
419



424
327



425
380



426
388



427
434



428
397



429
428



430
440



431
470



432
345



433
390



434
403



435
438



436
411



437
445



438
453



439
475



440
417



441
450



442
459



443
485



444
465



445
479



446
488



447
504



448
260



449
304



450
323



451
378



452
339



453
387



454
394



455
436



456
357



457
404



458
400



459
448



460
414



461
442



462
454



463
480



464
365



465
406



466
420



467
457



468
427



469
452



470
467



471
483



472
435



473
469



474
460



475
486



476
474



477
491



478
493



479
502



480
384



481
424



482
432



483
461



484
443



485
466



486
471



487
489



488
449



489
472



490
481



491
496



492
476



493
490



494
498



495
507



496
456



497
484



498
478



499
494



500
487



501
501



502
497



503
506



504
492



505
499



506
503



507
508



508
505



509
509



510
510



511
511










Sequence Z28, having a sequence length of 256:

    • [0, 1, 4, 9, 2, 11, 7, 24, 3, 14, 17, 27, 10, 33, 34, 59, 5, 16, 12, 30, 21, 35, 43, 64, 20, 45, 37, 70, 49, 76, 81, 121, 6, 15, 23, 39, 18, 44, 40, 72, 26, 47, 54, 78, 57, 87, 90, 124, 31, 51, 60, 88, 66, 95, 99, 134, 73, 102, 109, 141, 113, 149, 155, 194, 8, 22, 19, 46, 32, 50, 56, 86, 28, 63, 52, 91, 67, 97, 103, 137, 38, 58, 69, 106, 75, 100, 108, 145, 82, 117, 120, 152, 128, 162, 167, 201, 42, 71, 79, 116, 84, 112, 123, 158, 92, 125, 135, 163, 138, 170, 176, 206, 101, 131, 143, 175, 147, 178, 185, 210, 159, 183, 190, 215, 196, 222, 227, 243, 13, 25, 36, 61, 29, 68, 55, 104, 41, 65, 74, 110, 80, 118, 122, 156, 48, 77, 83, 114, 89, 129, 132, 164, 98, 127, 136, 169, 146, 179, 184, 208, 53, 85, 96, 130, 93, 133, 140, 174, 107, 142, 151, 181, 157, 186, 193, 217, 115, 150, 160, 187, 166, 191, 197, 220, 172, 202, 205, 224, 212, 230, 235, 247, 62, 94, 105, 144, 111, 148, 154, 188, 119, 153, 161, 195, 168, 200, 204, 225, 126, 165, 171, 199, 177, 203, 209, 229, 182, 211, 214, 232, 219, 236, 238, 249, 139, 173, 180, 207, 189, 213, 216, 233, 192, 221, 223, 237, 226, 239, 241, 250, 198, 218, 228, 240, 231, 242, 244, 251, 234, 245, 246, 252, 248, 253, 254, 255]












Table Z28, having a sequence length of 256:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
4



3
9



4
2



5
11



6
7



7
24



8
3



9
14



10
17



11
27



12
10



13
33



14
34



15
59



16
5



17
16



18
12



19
30



20
21



21
35



22
43



23
64



24
20



25
45



26
37



27
70



28
49



29
76



30
81



31
121



32
6



33
15



34
23



35
39



36
18



37
44



38
40



39
72



40
26



41
47



42
54



43
78



44
57



45
87



46
90



47
124



48
31



49
51



50
60



51
88



52
66



53
95



54
99



55
134



56
73



57
102



58
109



59
141



60
113



61
149



62
155



63
194



64
8



65
22



66
19



67
46



68
32



69
50



70
56



71
86



72
28



73
63



74
52



75
91



76
67



77
97



78
103



79
137



80
38



81
58



82
69



83
106



84
75



85
100



86
108



87
145



88
82



89
117



90
120



91
152



92
128



93
162



94
167



95
201



96
42



97
71



98
79



99
116



100
84



101
112



102
123



103
158



104
92



105
125



106
135



107
163



108
138



109
170



110
176



111
206



112
101



113
131



114
143



115
175



116
147



117
178



118
185



119
210



120
159



121
183



122
190



123
215



124
196



125
222



126
227



127
243



128
13



129
25



130
36



131
61



132
29



133
68



134
55



135
104



136
41



137
65



138
74



139
110



140
80



141
118



142
122



143
156



144
48



145
77



146
83



147
114



148
89



149
129



150
132



151
164



152
98



153
127



154
136



155
169



156
146



157
179



158
184



159
208



160
53



161
85



162
96



163
130



164
93



165
133



166
140



167
174



168
107



169
142



170
151



171
181



172
157



173
186



174
193



175
217



176
115



177
150



178
160



179
187



180
166



181
191



182
197



183
220



184
172



185
202



186
205



187
224



188
212



189
230



190
235



191
247



192
62



193
94



194
105



195
144



196
111



197
148



198
154



199
188



200
119



201
153



202
161



203
195



204
168



205
200



206
204



207
225



208
126



209
165



210
171



211
199



212
177



213
203



214
209



215
229



216
182



217
211



218
214



219
232



220
219



221
236



222
238



223
249



224
139



225
173



226
180



227
207



228
189



229
213



230
216



231
233



232
192



233
221



234
223



235
237



236
226



237
239



238
241



239
250



240
198



241
218



242
228



243
240



244
231



245
242



246
244



247
251



248
234



249
245



250
246



251
252



252
248



253
253



254
254



255
255










Sequence Z29, having a sequence length of 128:

    • [0, 1, 4, 9, 2, 11, 7, 23, 3, 13, 16, 25, 10, 30, 31, 51, 5, 15, 12, 27, 20, 32, 38, 54, 19, 40, 33, 58, 43, 63, 66, 90, 6, 14, 22, 35, 17, 39, 36, 60, 24, 42, 47, 64, 49, 70, 72, 92, 28, 45, 52, 71, 55, 75, 77, 96, 61, 80, 84, 100, 86, 104, 106, 119, 8, 21, 18, 41, 29, 44, 48, 69, 26, 53, 46, 73, 56, 76, 81, 98, 34, 50, 57, 82, 62, 78, 83, 102, 67, 88, 89, 105, 94, 109, 111, 121, 37, 59, 65, 87, 68, 85, 91, 107, 74, 93, 97, 110, 99, 112, 114, 122, 79, 95, 101, 113, 103, 115, 117, 123, 108, 116, 118, 124, 120, 125, 126, 127]












Table Z29, having a sequence length of 128:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
4



3
9



4
2



5
11



6
7



7
23



8
3



9
13



10
16



11
25



12
10



13
30



14
31



15
51



16
5



17
15



18
12



19
27



20
20



21
32



22
38



23
54



24
19



25
40



26
33



27
58



28
43



29
63



30
66



31
90



32
6



33
14



34
22



35
35



36
17



37
39



38
36



39
60



40
24



41
42



42
47



43
64



44
49



45
70



46
72



47
92



48
28



49
45



50
52



51
71



52
55



53
75



54
77



55
96



56
61



57
80



58
84



59
100



60
86



61
104



62
106



63
119



64
8



65
21



66
18



67
41



68
29



69
44



70
48



71
69



72
26



73
53



74
46



75
73



76
56



77
76



78
81



79
98



80
34



81
50



82
57



83
82



84
62



85
78



86
83



87
102



88
67



89
88



90
89



91
105



92
94



93
109



94
111



95
121



96
37



97
59



98
65



99
87



100
68



101
85



102
91



103
107



104
74



105
93



106
97



107
110



108
99



109
112



110
114



111
122



112
79



113
95



114
101



115
113



116
103



117
115



118
117



119
123



120
108



121
116



122
118



123
124



124
120



125
125



126
126



127
127










Sequence Z30, having a sequence length of 64:

    • [0, 1, 4, 8, 2, 10, 7, 20, 3, 12, 15, 22, 9, 25, 26, 39, 5, 14, 11, 23, 18, 27, 31, 41, 17, 33, 28, 43, 35, 46, 48, 57, 6, 13, 19, 29, 16, 32, 30, 44, 21, 34, 37, 47, 38, 49, 51, 58, 24, 36, 40, 50, 42, 52, 53, 59, 45, 54, 55, 60, 56, 61, 62, 63]












TABLE Z30, having a sequence length of 64:










Polarized channel
Reliability or sequence



sequence number
number of reliability














0
0



1
1



2
4



3
8



4
2



5
10



6
7



7
20



8
3



9
12



10
15



11
22



12
9



13
25



14
26



15
39



16
5



17
14



18
11



19
23



20
18



21
27



22
31



23
41



24
17



25
33



26
28



27
43



28
35



29
46



30
48



31
57



32
6



33
13



34
19



35
29



36
16



37
32



38
30



39
44



40
21



41
34



42
37



43
47



44
38



45
49



46
51



47
58



48
24



49
36



50
40



51
50



52
42



53
52



54
53



55
59



56
45



57
54



58
55



59
60



60
56



61
61



62
62



63
63










It should be noted that, the foregoing sequences are merely some examples. Use of the foregoing sequences in a polar code encoding process helps improve encoding/decoding performance of a polar code. In any one of the sequences described, adjustments or equivalent replacements in the following aspects may be made without affecting an overall effect.


1. Positions of a small quantity of elements in a sequence are interchanged. For example, a position of a sequence number may be adjusted within a specified range. For example, the specified range is 5, and a position of an element whose sequence number is 10 may be adjusted within five positions to the left or right.


2. Some of the elements in the sequence are adjusted, but channel sets for transmitting T bit information that are selected based on the sequence are consistent or similar.


3. The sequence includes N elements starting from 0 and ending with N−1, and the N elements starting from 0 and ending with N−1 represent sequence numbers of N polarized channels. Actually, the sequence numbers of the N polarized channels may also start from 1 and end with N. This can be achieved by adding 1 to each sequence number in the foregoing sequence, and this is also a sequence number form in the foregoing calculation manners. Certainly, the sequence number or an identifier of the foregoing polarized channel may also be represented by using another manner. The specific representation manner does not affect a specific position of a polarized channel in a sequence;


4. The sequence numbers of the N polarized channels in the foregoing sequence are arranged in ascending order of the reliability of the N polarized channels. In this case, selecting K polarized channels in descending order of reliability is selecting polarized channels that correspond to the last K sequence numbers in any of the foregoing sequences. Actually, the sequence numbers of the N polarized channels may also be arranged in descending order of the reliability of the N polarized channels. This can be achieved by arranging the elements in the foregoing sequence in a reverse or inverted order. In this case, selecting K polarized channels in descending order of reliability is selecting polarized channels that correspond to the first K sequence numbers; and


5. The foregoing sequences may further be represented by using a normalized reliability or an equivalent reliability of each channel. For example, if a sequential position of a channel x in the foregoing sequence is n (a leftmost position is denoted as 1), a reliability of the channel may be represented as n or normalized n/N, where N is a length of the sequence.


Based on a same invention concept of the polar code encoding method shown in FIG. 2, as shown in FIG. 3, an embodiment of this application further provides a polar code encoding apparatus 300. The polar code encoding apparatus 300 is configured to perform the polar code encoding method shown in FIG. 2. Part or all of the polar code encoding method shown in FIG. 3 may be implemented by using hardware or may be implemented by using software. When part or all of the polar code encoding method is implemented by using hardware, the polar code encoding apparatus 300 includes: an input interface circuit 301, configured to obtain to-be-encoded bits; a logic circuit 302, configured to perform the polar code encoding method shown in FIG. 2, where for details, refer to the descriptions in the foregoing method embodiments, and details are not described herein again; and an output interface circuit 303, configured to output a bit sequence after encoding.


Further, the bit sequence that is obtained after the encoding and that is output by the encoding apparatus 300 is output to a transceiver 320 after being modulated by a modulator 310. The transceiver 320 performs corresponding processing (including but not limited to processing such as digital-to-analog conversion and/or frequency conversion) on the modulated sequence and sends the processed sequence by using an antenna 330.


Optionally, the polar code encoding apparatus 300 may be a chip or an integrated circuit during specific implementation.


Optionally, when part or all of the polar code encoding method in the foregoing embodiment is implemented by using software, as shown in FIG. 4, the polar code encoding apparatus 300 includes: a memory 401, configured to store a program; a processor 402, configured to execute the program stored in the memory 401. When the program is executed, the polar code encoding apparatus 300 is caused to implement the polar code encoding method provided in the embodiment in FIG. 2.


Optionally, the memory 401 may be a physically independent unit. Alternatively, as shown in FIG. 5, a memory 501 is integrated with a processor 502.


Optionally, when part of or all of the encoding method in the embodiment in FIG. 2 is implemented by using software, the polar code encoding apparatus 300 may include only the processor 402. The memory 401 configured to store the program is located outside the polar code encoding apparatus 300. The processor 402 is connected to the memory 401 by using a circuit/wire and is configured to read and execute the program stored in the memory 401.


The processor 402 may be a central processing unit (CPU), a network processor (NP), or a combination of a CPU and an NP.


The processor 402 may further include a hardware chip. The foregoing hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination of an ASIC and a PLD. The foregoing PLD may be a complex programmable logical device (CPLD), a field-programmable gate array (FPGA), a generic array logic (GAL), or any combination thereof.


The memory in the foregoing embodiment may include a volatile memory, for example, a random-access memory (RAM). Alternatively, the memory may include a non-volatile memory, for example, a flash memory, a hard disk drive (HDD), or a solid-state drive (SSD). Alternatively, the memory may include a combination of the foregoing types of memories.


Based on the polar code encoding method shown in FIG. 2, as shown in FIG. 6, an embodiment of this application further provides a polar code encoding apparatus 300. The polar code encoding apparatus 300 is configured to perform the polar code encoding method shown in FIG. 2. The polar code encoding apparatus 300 includes:

    • an obtaining unit 601, configured to obtain a first sequence used to encode K to-be-encoded bits, where the first sequence includes sequence numbers of N polarized channels, the sequence numbers of the N polarized channels are arranged in the first sequence based on reliability of the N polarized channels, K is a positive integer, N is a mother code length of a polar code, N is a positive integer power of 2, and K≤N;
    • a selection unit 602, configured to select sequence numbers of K polarized channels from the first sequence in ascending order of the reliability; and
    • an encoding unit 603, configured to place the to-be-encoded bits based on the selected sequence numbers of the K polarized channels, and perform polar code encoding on the to-be-encoded bits.


The first sequence may be any one of the sequences described above, or may be a sequence obtained by selecting, from a second sequence having a length of Nmax, sequence numbers (starting from 0) less than N. The second sequence may be any one of the sequences described above. A reliability of an ith polarized channel in the N polarized channels may be determined by using any one of the formulas described above.


An embodiment of this application further provides a computer storage medium storing a computer program. The computer program is configured to perform the polar code encoding method shown in FIG. 2.


An embodiment of this application further provides a computer program product including an instruction. When run on a computer, the instruction causes the computer to perform the polar code encoding method shown in FIG. 2.


Persons skilled in the art should understand that the embodiments of this application may be provided as a method, a system, or a computer program product. Therefore, this application may use a form of hardware only embodiments, software only embodiments, or embodiments with a combination of software and hardware. Moreover, this application may use a form of a computer program product that is implemented on one or more computer-usable storage media (including but not limited to a disk memory, a CD-ROM, an optical memory, and the like) that include computer usable program code.


This application is described with reference to the flowcharts and/or block diagrams of the method, the device (system), and the computer program product according to the embodiments of this application. It should be understood that computer program instructions may be used to implement each process and/or each block in the flowcharts and/or the block diagrams and a combination of a process and/or a block in the flowcharts and/or the block diagrams. These computer program instructions may be provided for a general-purpose computer, a dedicated computer, an embedded processor, or a processor of any other programmable data processing device to generate a machine, so that the instructions executed by a computer or a processor of any other programmable data processing device generate an apparatus for implementing a specific function in one or more processes in the flowcharts and/or in one or more blocks in the block diagrams.


These computer program instructions may be stored in a computer readable memory that can instruct the computer or any other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory generate an artifact that includes an instruction apparatus. The instruction apparatus implements a specific function in one or more processes in the flowcharts and/or in one or more blocks in the block diagrams.


These computer program instructions may be loaded onto a computer or another programmable data processing device, so that a series of operations and steps are performed on the computer or the another programmable device, thereby generating computer-implemented processing. Therefore, the instructions executed on the computer or the another programmable device provide steps for implementing a specific function in one or more processes in the flowcharts and/or in one or more blocks in the block diagrams.


Although some preferred embodiments of this application have been described, persons skilled in the art can make changes and modifications to these embodiments once they learn the basic inventive concept. Therefore, the following claims are intended to be construed as to cover the preferred embodiments and all changes and modifications falling within the scope of this application.


Obviously, persons skilled in the art can make various modifications and variations to the embodiments of this application without departing from the spirit and scope of the embodiments of this application. This application is intended to cover these modifications and variations provided that they fall within the scope of protection defined by the following claims and their equivalent technologies.

Claims
  • 1. An encoding method, comprising: obtaining, by an encoding apparatus, a first sequence used to encode K to-be-encoded bits, the first sequence comprising reliability sequence numbers of N polarized channels, K is a positive integer, K≤N, N=1024;selecting, by the encoding apparatus, reliability sequence numbers of K polarized channels from the first sequence;performing, by the encoding apparatus, polar code encoding on the K to-be-encoded bits based on the selected reliability sequence numbers of the K polarized channels and generating a polar code encoded bit sequence; andoutputting, by the encoding apparatus, the polar code encoded bit sequence to a receiving device;the first sequence comprising Sequence Z11 or Table Z11.
  • 2. The method according to claim 1, wherein the reliability sequence numbers of the N polarized channels are arranged in the first sequence based on sequence number of the N polarized channels.
  • 3. The method according to claim 1, wherein the reliability sequence numbers of the K polarized channels are selected based on reliability of the N polarized channels.
  • 4. The method according to claim 1, wherein the K to-be-encoded bits comprise a cyclic redundancy check (CRC) bit.
  • 5. The method according to claim 1, wherein the K to-be-encoded bits comprise a parity check (PC) bit.
  • 6. The method according to claim 1, wherein after performing the polar code encoding on the to-be-encoded bits, the encoding apparatus performs, based on a target code length, rate matching on the polar code encoded bit sequence, wherein the outputting the polar code encoded bit sequence comprises outputting the polar code encoded bit sequence after rate matching.
  • 7. A polar code encoding apparatus, comprising: a memory storage comprising instructions; anda processor in communication with the memory, wherein the processor is configured to execute the instructions to perform the steps:obtaining a first sequence used to encode K to-be-encoded bits, the first sequence comprising reliability sequence numbers of N polarized channels, K is a positive integer, K≤N, N=1024;selecting reliability sequence numbers of K polarized channels from the first sequence;performing polar code encoding on the K to-be-encoded bits based on the selected reliability sequence numbers of the K polarized channels and generating a polar code encoded bit sequence; andoutputting, by the encoding apparatus, the polar code encoded bit sequence to a receiving device;the first sequence comprising Sequence Z11 or Table Z11.
  • 8. The apparatus according to claim 7, wherein the reliability sequence numbers of the N polarized channels are arranged in the second sequence based on sequence number of the N polarized channels.
  • 9. The apparatus according to claim 7, wherein the reliability sequence numbers of the K polarized channels are selected based reliability of the N polarized channels.
  • 10. The apparatus according to claim 7, wherein the K to-be-encoded bits comprise a cyclic redundancy check (CRC) bit.
  • 11. The apparatus according to claim 7, wherein the K to-be-encoded bits comprise a parity check (PC) bit.
  • 12. The apparatus according to claim 7, wherein the processor is further configured to execute the instructions to perform: rate matching on the polar code encoded bit sequence based on a target code length, and output the polar code encoded bit sequence after rate matching.
  • 13. An apparatus, comprising: an input interface circuit, configured to obtain K to-be-encoded bits;a logic circuit, configured to:obtain, by an encoding apparatus, a first sequence used to encode K to-be-encoded bits, the first sequence comprising reliability sequence numbers of N polarized channels, K is a positive integer, K≤N, N=1024;select, by the encoding apparatus, reliability sequence numbers of K polarized channels from the first sequence;perform, by the encoding apparatus, polar code encoding on the K to-be-encoded bits based on the selected reliability sequence numbers of the K polarized channels and generate a polar code encoded bit sequence; andan output interface circuit configured to output the polar code encoded bit sequence to a receiving device;the first sequence comprising Sequence Z11 or Table Z11.
  • 14. The apparatus according to claim 13, wherein the reliability sequence numbers of the Nmax polarized channels are arranged in the second sequence based on sequence number of the Nmax polarized channels.
  • 15. The apparatus according to claim 13, wherein the reliability sequence numbers of the K polarized channels are selected based on reliability of the N polarized channels.
  • 16. The apparatus according to claim 13, wherein the K to-be-encoded bits comprise a cyclic redundancy check (CRC) bit.
  • 17. The apparatus according to claim 13, wherein the K to-be-encoded bits comprise a parity check (PC) bit.
  • 18. The apparatus according to claim 13, wherein the logic circuit is further configured to rate match on the polar code encoded bit sequence based on a target code length, and the output interface circuit is configured to output the polar code encoded bit sequence after rate matching.
Priority Claims (1)
Number Date Country Kind
201710653644.4 Aug 2017 CN national
CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No. 16/838,945, filed on Apr. 2, 2020, which is a continuation of U.S. patent application Ser. No. 16/145,850, filed on Sep. 28, 2018, now U.S. Pat. No. 10,659,194, which is a continuation of International Application No. PCT/CN2018/085567, filed on May 4, 2018. The International Application claims priority to Chinese Patent Application No. 201710653644.4, filed on Aug. 2, 2017. All of the afore-mentioned patent applications are hereby incorporated by reference in their entireties.

US Referenced Citations (14)
Number Name Date Kind
10659194 Wang May 2020 B2
11165535 Wang Nov 2021 B2
20040186809 Schlesinger Sep 2004 A1
20080209286 Hamada Aug 2008 A1
20140169492 Mahdavifar et al. Jun 2014 A1
20140331083 Aliev et al. Nov 2014 A1
20150103947 Shen et al. Apr 2015 A1
20150194987 Li et al. Jul 2015 A1
20160013810 Gross et al. Jan 2016 A1
20170077954 Shen et al. Mar 2017 A1
20170111060 Huang et al. Apr 2017 A1
20170213047 Huang et al. Jul 2017 A1
20180026663 Wu Jan 2018 A1
20180331697 Lin Nov 2018 A1
Foreign Referenced Citations (48)
Number Date Country
102577559 Jul 2012 CN
102694625 Sep 2012 CN
103023518 Apr 2013 CN
103281166 Sep 2013 CN
103684477 Mar 2014 CN
103733560 Apr 2014 CN
103746708 Apr 2014 CN
103959826 Jul 2014 CN
104539393 Apr 2015 CN
105009541 Oct 2015 CN
105099622 Nov 2015 CN
105743621 Jul 2016 CN
106506079 Mar 2017 CN
106877973 Jun 2017 CN
106899379 Jun 2017 CN
107592181 Jan 2018 CN
108347300 Jul 2018 CN
108390740 Aug 2018 CN
108631942 Oct 2018 CN
108667568 Oct 2018 CN
108809333 Nov 2018 CN
108880743 Nov 2018 CN
109150384 Jan 2019 CN
109257140 Jan 2019 CN
109286402 Jan 2019 CN
109286403 Jan 2019 CN
109286404 Jan 2019 CN
109347488 Feb 2019 CN
109391343 Feb 2019 CN
104685923 Jul 2019 CN
2899911 Jul 2015 EP
2563568 Dec 2018 GB
20110060635 Jun 2011 KR
20180108373 Oct 2018 KR
20180137356 Dec 2018 KR
2571587 Dec 2015 RU
2012149559 Nov 2012 WO
2013025547 Feb 2013 WO
2014000532 Jan 2014 WO
2015000511 Jan 2015 WO
2015006947 Jan 2015 WO
2016082142 Jun 2016 WO
2016101089 Jun 2016 WO
2017092693 Jun 2017 WO
2017097098 Jun 2017 WO
2017101631 Jun 2017 WO
2017197358 Nov 2017 WO
2018120734 Jul 2018 WO
Non-Patent Literature Citations (43)
Entry
Intel Corporation, Polar code design. 3GPP TSG RAN WG1 Ad hoc, Spokane, USA, Jan. 16-20, 2017, R1-1700386, 12 pages.
Kai Niu et al., Polar codes: Primary concepts and practical decoding algorithms. IEEE Communications Magazine ( vol. 52, Issue: 7, Jul. 2014), Jul. 15, 2014, 12 pages.
Bo Yuan el aL,“Successive Cancellation Decoding of Polar Codes using Stochastic Computing”,2015 IEEE International Symposium on Circuits and Systems (ISCAS),total 4 pages.
Huawei et al,“Channel coding chain for control channel”, 3GPP TSG RAN WG1 RAN1#89 Meeting R 1-1706968, Hangzhou, China, May 15-19, 2017,total 4 pages.
Huawei et al.,“Channel coding chain for control channel”,3GPP TSG RAN WG1 NR Ad-Hoc#2, R1-1710003, Qingdao, China, Jun. 27-30, 2017,total 4 pages.
NTT DOCOMO,“Discussion on construction of Polar codes”,3GPP TSG RAN WG1 Meeting#88, R1-1702850, Athens, Greece, Feb. 13-17, 2017,total 9 pages.
Samsung,“Design of a Nested Sequence for Polar Codes”,3GPP TSG RAN WG1#8Bbis, R1-1705425, Spokane, WA, Apr. 3-7, 2017,total 8 pages.
Qualcomm Incorporated,“FRANK polar construction: nested extension design of polar codes based on mutual information”,3GPP TSG-RAN WG1#88b, R1-1705633, Apr. 3-7, 2017,Spokane, USA. total 21 pages.
NTT DOCOMO,“Sequence design of Polar codes”, 3GPP TSG RAN WG1 Meeting #88bis, R1-1705758, Spokane, USA, Apr. 3-7, 2017, total 5 pages.
Samsung,“Design of rate-matching polar code”,3GPP TSG RAN WG1 Meeting#88bis, R1-1706814, Spokane, WA, Apr. 3-7, 2017, total 10 pages.
NEC,“Evaluation of sequence design for polar codes”,3GPP TSG RAN WG1 Meeting #89, R1-1707059, Hangzhou, China, May 15-20, 2017, total 5 pages.
LG Electronics,“Information bit allocation of Polar codes”,3GPP TSG RAN WG1 Meeting#89, R1-1707674, Hangzhou, China, May 15-19, 2017, total 5 pages.
LG Electronics,“Discussion of rate matching for Polar codes”, 3GPP TSG RAN WG1 Meeting#88bis, R1-1707675, Hangzhou, China, May 15-19, 2017, total 5 pages.
Samsung,“Design of a Nested polar code sequences”, 3GPP TSG RAN WG1 Meeting#89, R1-1708051, Hangzhou, P. R. China May 15-19, 2017, total 3 pages.
NTT DOCOMO,“Sequence design of Polar codes”, 3GPP TSG RAN WG1 Meeting #89, R1-1708489, Hangzhou, China, May 15-19, 2017, total 6 pages.
Qualcomm Incorporated,“FRANK polar construction for NR control channel and performance comparison”,3GPP TSG-RAN WG1#89, R1-1708646, May 15-19, 2017,Hangzhou, P. R China, total 22 pages.
Nokia et al.,“Sequence design for Polar codes”, 3GPP TSG RAN WG1 Meeting #89, R1-1708834, Hangzhou, P.R, China May 15-19, 2017,total 13 pages.
Samsung,“Design of Combined-and-Nested Polar Code Sequences”,3GPP TSG RAN WG1 NR Ad-Hoc #2, R1-1710749, Qingdao, P.R. China, Jun. 27-30, 2017,total 18 pages.
NTT DOCOMO,“Sequence design of Polar codes”,3GPP TSG RAN WG1 NR Ad-Hoc#2, R1-1711126, Qingdao, China, Jun. 27-30, 2017, total 6 pages.
Qualcomm Incorporated,“Sequence construction of Polar codes for control channel”,3GPP TSG-RAN WG1 NR Ad-Hoc#2, R1-1711218, Jun. 27-30, 2017,Qingdao, P. R China ,total 17 pages.
Nokia et al.,“Sequence design for Polar codes”, 3GPP TSG RAN WG1 NR Ad-Hoc #2, R1-1711542, Qingdao, P.R. China Jun. 27-30, 2017, total 13 pages.
3GPP TSG-RAN WG1 NR AdHoc, R1-1700832, Qualcomm Incorporated:“Design of Polar codes for control channel”, Jan. 16-20, 2017, Spokane, USA, 5 pages. XP51208351.
3GPP TSG RAN WG1#8Bbis, R1-1705425, Samsung:“Design of a Nested Sequence for Polar Codes”, Spokane, WA, Apr. 3-7, 2017. 8 pages. XP51243555.
3GPP TSG RAN WG1 NR Ad-Hoc#-2, R1-1710003, Huawei, HiSilicon:“Channel coding chain for control channel”, Qingdao, China, Jun. 27-30, 2017, 4 pages, XP51299228.
3GPP TSG RAN WG1 Meeting #89, R1-1708489, NTT DOCOMO:“Sequence design of Polar codes”, Hangzhou, China May 15-19, 2017. 6 pages. XP51273681.
3GPP TS 38.212 V15.0.0 (Dec. 2017), 3rd Generation Partnership Project;Technical Specification Group Radio Access Network; NR; Multiplexing and channel coding(Release 15), total 23 pages.
Huawei, HiSilicon, Polar code design and rate matching . 3GPP TSG RAN WG1 Meeting #86, Gothenburg, Sweden, Aug. 22-26, 2016, R1-167209, 5 pages.
Huawei, HiSilicon, Construction schemes for polar codes. 3GPP TSG RAN WG1 Meeting #88, Athens, Greece, Feb. 13-17, 2017, R1-1701702, 7 pages.
Huawei, HiSilicon, Overview of Polar Codes. 3GPP TSG RAN WG1 Meeting #84bis, Busan, Korea, Apr. 11-15, 2016, R1-162161, 7 pages.
3GPP TS 36.101 V10.9.0 (Dec. 2012), 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); User Equipment (UE) radio transmission and reception(Release 10), 361 pages.
Huawei, HiSilicon, Summary of polar code design for control channels[online], 3GPP TSG RAN WG1 Ad-Hoc Meeting R1-1700088, Jan. 20, 2017,total 12 pages.
3GPP TS 36.211 V10.1.0 (Mar. 2011), 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical Channels and Modulation(Release 10), 103 pages.
3GPP TS 36.211 V10.6.0 (Dec. 2012), 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical Channels and Modulation(Release 10), 101 pages.
3GPP TS 36.212 V10.7.0 (Dec. 2012), 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Multiplexing and channel coding(Release 10), 79 pages.
3GPP TS 36.213 V10.1.0 (Mar. 2011), 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical layer procedures(Release 10), 115 pages.
3GPP TS 36.213 V10.8.0 (Dec. 2012), 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical layer procedures(Release 10), 126 pages.
3GPP TS 36.213 V11.2.0 (Feb. 2012), 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical layer procedures(Release 11), 173 pages.
3GPP TS 36.321 V10.8.0 (Mar. 2013), 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Medium Access Control (MAC) protocol specification (Release 10), 54 pages.
3GPP TS 36.331 V10.1.0 (Mar. 2011), 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Radio Resource Control (RRC); Protocol specification (Release 10), 290 pages.
3GPP TS 36.331 V10.8.0 (Dec. 2012), 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Radio Resource Control (RRC); Protocol specification (Release 10), 305 pages.
3GPP TS 36.331 V11.3.0 (Mar. 2013), 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Radio Resource Control (RRC); Protocol specification (Release 11), 343 pages.
Shenzukang,[NRAH2-11]Polar code sequence. Jul. 12, 2017, 110 pages.
3GPP TS 36.213 V11.2.0 (Feb. 2013), 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical layer procedures(Release 11), 173 pages.
Related Publications (1)
Number Date Country
20220109524 A1 Apr 2022 US
Continuations (3)
Number Date Country
Parent 16838945 Apr 2020 US
Child 17491529 US
Parent 16145850 Sep 2018 US
Child 16838945 US
Parent PCT/CN2018/085567 May 2018 US
Child 16145850 US