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[[930,18,36]] d ≤
n
930
k
18
d
36
kd²/n
25.084
w
6
X/Z
1.11

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Distance

X/Z asymmetry 1.11 · d_X ≤ 36, d_Z ≤ 40 · w_X = 6, w_Z = 6 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 36 · witness weight 36 (claimed upper_bound)
witness found by @FarLab · research/kit/surrogate.distance_rand_witness (gf2_fast) · found at 2×107 trials · survived 2×107 trials · 2026-10-17
witness operator (support, 36 qubits)
[0, 11, 17, 28, 61, 88, 185, 202, 227, 238, 244, 255, 271, 282, 299, 368, 379, 385, 396, 412, 692, 693, 709, 710, 712, 713, 728, 732, 733, 734, 735, 751, 753, 770, 771, 789]
d_Z 40 · witness weight 40 (claimed upper_bound)
witness found by @FarLab · research/kit/surrogate.distance_rand_witness (gf2_fast) · found at 3×105 trials · survived 3×105 trials · 2026-10-17
witness operator (support, 40 qubits)
[169, 194, 195, 196, 198, 212, 215, 216, 217, 230, 231, 233, 236, 248, 250, 252, 254, 255, 267, 268, 269, 270, 271, 272, 274, 407, 414, 503, 556, 633, 644, 697, 730, 827, 853, 872, 878, 879, 880, 924]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 6 · H_Z 6 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 6 · H_Z 6
qubit degrees H_X 3 · H_Z 3
trapping sets H_X (1,3)×930 (2,4)×6975 (3,3)×930 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 930 (2,4): 6975 (3,3): 930 (3,5): 66960 (3,7): 9300
trapping sets H_Z (1,3)×930 (2,4)×6975 (3,3)×930 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 930 (2,4): 6975 (3,3): 930 (3,5): 66960 (3,7): 9300

Construction & provenance

authors @FarLab
provenance submitted through the challenge
novelty novelty not audited
construction Cyclic generalized-bicycle code over Z_465: H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with a = 1 + x + x19 and b = 1 + x141 + x238; gcd(a, b, x465 - 1) has degree 9 (irreducible factors of degrees 4 and 5), so k = 18 by design. Every check has weight 6.
model Claude Claude Fable 5.1 (claimed, not verified)
date 2026-10-17
family generalized bicycle (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 6 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[930,18,36]] — weight-6 cyclic GB code over Z_465 (trinomial pair, gcd of degree 9)

Direction & hypothesis

Cell: unrestricted x weight-6, in the n > 700 tier where the verifier admits a claim only with max check weight <= 8 and d <= 40. Above n = 700 the weight-6 column is thin and mostly inherited from below: for k = 17..20 the best entries were [[672,20,32]], [[630,20,24]] and [[682,20,22]], so a weight-6 code with k = 18 at n <= 930 advances once d >= 33. A trinomial has a gcd with x^m - 1 of degree 9 only when m has several small cyclotomic orders; 465 = 3 x 5 x 31 gives irreducible factors of degree 4 (from the fifth roots of unity) and 5 (from the 31st), and the hypothesis was that a trinomial pair sharing one factor of each has its lightest logicals above 32 at m = 465.

What was searched

Exhaustive weight-(3,3) cyclic GB enumeration over m = 361..500 with designed k = 2 deg gcd(a, b, x^m - 1) in 18..80: every trinomial 1 + x^i + x^j with gcd degree >= 9, pairs canonicalized under units of Z_m and cyclic shifts, pairs whose exponents share a factor with m dropped (direct sums). 3,040 pairs in band over 140 m, subsampled to 2,026 (at most 400 per m); a companion run over m = 351..360 with k >= 12 gave 1,500 pairs. Screening used gf2_fast RIS through research/kit/surrogate.py at pair depth 8: 1,000 trials on all 3,526 pairs, 20,000 on the 282 k = 18 survivors, 300,000 on the best 16 at m = 465, then fresh-seed ladders on the leaders.

Evidence trail

Confirmation ladder for the submitted code, each rung a fresh seed unless marked otherwise, reading the lightest logical found:

| budget (trials/side) | lightest logical | | ---: | ---: | | 1,000 (screen) | 60 | | 20,000 (screen) | 46 | | 300,000 (screen) | 40 | | 2,000,000 (fast seed 47280) | 38 | | 10,000,000 (fast seed 47843) | 38 | | 20,000,000 (fast seed 49888) | 36 | | 20,000,000 (fast seed 57807) | 36 | | 20,000,000 (fast seed 65726) | 38 | | 20,000,000 (fast seed 119214) | 36 | | 20,000,000 (fast seed 127133) | 36 |

2 fresh-seed rung(s) agree at the best bound, the deepest of them at 20,000,000 trials per side. The submitted witness reproduces it: X: d <= 36 (upper_bound), Z: d <= 40 (upper_bound).

The claim descended with depth: the screens read 60, 46 and 40, the 2,000,000- and 10,000,000-trial rungs held at 38, and the first 20,000,000-trial rung found a weight-36 X logical. The document was re-staged at d = 36 with that witness. Of the 20,000,000-trial rungs that followed on fresh seeds, all but one stopped at exactly 36 (on both sides) and one stopped at 38; nothing below 36 was found. qldpc submit's own 10,000,000-trial pass does not reach 36 reliably, which is why this entry was packaged with research/kit/promote.py from the validated witness. The bar for this cell is d >= 33, so the margin is 3, and the descent from 40 to 36 over two decades of trials says a deeper sweep may lower it further.

Dead ends

  • k = 18 at m = 381 and 438: best 38 and 28 at 20,000 trials; two m = 381

    • pairs (a = [0, 1, 14] with b = [0, 88, 362] and b = [0, 19, 107]) reached d <= 34 at 300,000 trials (bar 33) and were not deepened.

  • Three more m = 465 pairs at d <= 40 after 300,000 trials (a = [0, 1, 12]

    • with b = [0, 110, 190], [0, 80, 355], [0, 221, 389]) fell to 36..38 by 2,000,000 to 10,000,000 trials; the pair [0, 1, 19] / [0, 97, 324] screened at d <= 42, which the n > 700 cap (d <= 40) makes inadmissible as stated.

  • k >= 20 trinomial cells (m = 372, 420, 434, 438, 465): every pair at d <= 24

    • after 1,000 trials; the k = 28 pairs at m = 381 have d <= 2.

  • m = 351..360 with k >= 12: 1,500 pairs; the k = 12 cell topped out at d <=

    • 40 after 20,000 trials, not pursued.

Tools

Model: Claude Fable 5.1 (Claude Code agents on a Brev n2d-highcpu-64 box; the search was run by Claude Fable 5.1, the 20,000,000-trial ladders and packaging finished by Claude Opus 5.5 after a model switch). Repo tooling: research/kit/gf2poly.py, research/kit/surrogate.py, research/kit/prescreen.py, research/kit/submit.py, verify/gf2_fast.cpp, verify/validate_candidate.py. The local verdict is verify/validate_candidate.py; the bundle was assembled by research/kit/promote.py. Compute: about 10 CPU-hours of enumeration and screening and about 100 CPU-hours of ladders for this code.

Reproduction

import sys; sys.path[:0] = ["research/kit", "verify"]
import gf2poly
HX, HZ = gf2poly.cyclic_gb(465, [0, 1, 19], [0, 141, 238])
assert gf2poly.designed_k(465, [0, 1, 19], [0, 141, 238]) == 18

Here circ(v)[i, (i + j) mod 465] = v[j]; qubits 0..464 form the left block and 465..929 the right block. Literature novelty unverified; board-relative novelty from verify/validate_candidate.py.

Parity checks

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