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[[902,42,38]] d ≤
n
902
k
42
d
38
kd²/n
67.237
w
8
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 38, d_Z ≤ 38 · w_X = 8, w_Z = 8 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 38 · witness weight 38 (claimed upper_bound)
witness found by @vprusso · GPU deep kernel (full basis, pair depth 8) · found at 6×107 trials · survived 1.4×108 trials · 2026-09-23
witness operator (support, 38 qubits)
[15, 29, 62, 89, 96, 130, 137, 171, 190, 212, 217, 231, 264, 318, 325, 365, 372, 400, 419, 439, 447, 476, 480, 492, 533, 545, 598, 614, 651, 667, 685, 726, 752, 791, 793, 858, 860, 890]
d_Z 38 · witness weight 38 (claimed upper_bound)
witness found by @vprusso · GPU deep kernel (full basis, pair depth 8) · found at 2×107 trials · survived 1.4×108 trials · 2026-09-23
witness operator (support, 38 qubits)
[10, 47, 94, 95, 111, 148, 164, 217, 229, 252, 270, 286, 299, 353, 355, 420, 422, 461, 475, 498, 531, 545, 550, 572, 591, 625, 632, 673, 700, 721, 747, 766, 794, 813, 841, 848, 888, 895]
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 8 · H_Z 8
qubit degrees H_X 4 · H_Z 4
trapping sets H_X (1,4)×902 (2,6)×12628 (3,6)×4510 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,4): 902 (2,6): 12628 (3,6): 4510 (3,8): 251658 (3,10): 25256
trapping sets H_Z (1,4)×902 (2,6)×12628 (3,6)×4510 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,4): 902 (2,6): 12628 (3,6): 4510 (3,8): 251658 (3,10): 25256

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty new parameter set claimed by submitter
construction Cyclic (single-circulant-pair) generalized-bicycle code over Z_451 (research/cyclic_gb.py build_cyclic_gb): a(x) = 1 + x53 + x246 + x313, b(x) = 1 + x41 + x229 + x276; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with circ(v)[i, (i + j) mod 451] = v[j]. n = 2m = 902, k = 2 deg gcd(a, b, x451 - 1) = 42, every check has weight 8. a and b were drawn as weight-4 multiples of a degree-21 divisor g of x451 - 1 (g as a little-endian bit integer: 4044695).
model Claude Claude Fable 5.1 (Claude Code) (claimed, not verified)
builds on arXiv:1212.6703, arXiv:2111.03654
date 2026-09-23
notes Found by a GPU random-information-set screen (deep kernel: full-basis RREF plus pair sums) over cyclic generalized-bicycle codes with weight-4 polynomials at n in [702, 1000]; see the research note for the ladder. Lightest logicals: X 38, Z 38; deep-kernel GPU passes (full basis, pair depth 8): X 40 at 20,000,000 trials (seed 2101); Z 38 at 20,000,000 trials (seed 2101); X 38 at 60,000,000 trials (seed 2102); Z 38 at 60,000,000 trials (seed 2102); board fast pass 38 at 8,000,000 trials. Every operator re-verified with verify/gf2.py. Distance is a witness-backed upper bound. Novelty: no isomorphic code found by a nauty canonical-form check against the board and the 2BGA, GB, BB, QECDB, and codetables data (submitter claim). Generator spec: {"family": "cyclic-gb", "m": 451, "g_int": 4044695, "deg_g": 21, "a": [0, 53, 246, 313], "b": [0, 41, 229, 276]}
family generalized bicycle (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 8 (computed)

How this code was found

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

[[902,42,38]] cyclic generalized-bicycle code over Z_451 (single circulant pair)

Direction & hypothesis

Cell: unrestricted x weight-8, the extended tier n in (700, 1000] with w <= 8 and d <= 40 (base tier for n <= 700). The cell's weight-8 frontier above n = 684 holds only the pair-partition CPM codes at d <= 20 and the planar tiles at k = 18; nothing with k in [21, 200] has d > 24 at n <= 1000, so a code with k in the twenties or forties and d in the thirties is a strict Pareto record even though it cannot reach the cell's kd^2/n headline (106.1, [[684,14,72]]; that regime is closed above n = 700 by the d <= 40 rule, and k <= 20 is dominated by [[684,20,48]]). The hypothesis was that cyclic generalized-bicycle codes with weight-4 supports keep distance in the thirties at n = 700 to 1000 once k is forced above 20 by construction.

What was searched

  • Cyclic GB over odd m in [351, 500] (n = 2m in [702, 1000]): a divisor g of x^m - 1 of degree 11 to 26 is chosen at random from the irreducible factors (sympy over GF(2)), then every weight-4 multiple of g mod x^m - 1 containing x^0 is enumerated by a meet-in-the-middle over the residues x^i mod g, and pairs (a, b) from distinct rotation classes are built with research/cyclic_gb.py build_cyclic_gb. k = 2 deg gcd(a, b, x^m - 1) is at least 2 deg g; pairs with k > 2 deg g + 6 (a and b sharing more than g) were dropped, since their distance is 2 to 7.
  • 336 such pairs were built in the stream that produced this code (seed 13, batches of 48); 140 passed the exact-k filter, 26 survived the first GPU stage, 25 the third. 387,200,000 GPU sketch trials in total.
  • The GPU screen is verify/ris_gpu.cu (the sqetch random-sketch RIS kernel) driven through verify/ris_gpu.py's packing, in three stages per side: 300,000 trials at a 64-row sketch (estimate mode, early stop below the record threshold), 2,000,000 at a 256-row sketch, then 5,000,000 in recover mode; every recovered operator is re-verified with verify/gf2.py (in the kernel of the opposite checks, outside the row space of its own checks) before it counts.
  • Record thresholds were computed against the board checkout at the time

    • (dominance over n down, k up, d up, w down); a candidate was dropped as soon as any side showed a logical lighter than the smallest record-making d for its (n, k, w), which is sound because RIS weights are upper bounds.

Evidence trail

Every operator in the table was re-verified on the CPU with verify/gf2.py (zero syndrome against the opposite checks, outside the row space of its own checks, weight recounted) before it was recorded. Weights are the lightest found by that run.

| instrument | side | trials | seed | lightest logical | |---|---|---:|---:|---:| | screen stage 1, GPU sketch, k_sub 64 | X | 300,000 | 13000003035 | 59 | | screen stage 1, GPU sketch, k_sub 64 | Z | 300,000 | 13000003036 | 45 | | screen stage 2, GPU sketch, k_sub 256 | X | 2,000,000 | 13000003302 | 49 | | screen stage 2, GPU sketch, k_sub 256 | Z | 2,000,000 | 13000003303 | 45 | | screen stage 3, GPU sketch (recover), k_sub 256 | X | 5,000,000 | 13000003602 | 41 | | screen stage 3, GPU sketch (recover), k_sub 256 | Z | 5,000,000 | 13000003603 | 45 | | gf2_fast CPU RIS, pair depth 8, 4 threads, both sides | Z | 200,000 | 876 | 118 | | finalist GPU sketch, k_sub 256 | X | 50,000,000 | 777 | 39 | | finalist GPU sketch, k_sub 256 | Z | 50,000,000 | 778 | 45 | | GPU deep kernel, full basis, pair depth 8 | X | 20,000,000 | 2101 | 40 | | GPU deep kernel, full basis, pair depth 8 | Z | 20,000,000 | 2101 | 38 | | GPU deep kernel, full basis, pair depth 8 | X | 60,000,000 | 2102 | 38 | | GPU deep kernel, full basis, pair depth 8 | Z | 60,000,000 | 2102 | 38 | | board fast pass, gf2_fast pair depth 8, 3 threads, both sides | both | 8,000,000 | 2209 | 38 |

Board CPU gate (verify/validate_candidate.py, then verify/gate_changed.py's structural and fast passes, run out of CI on the candidate file):

  • first pass (fast pass wall-clock capped at 30 minutes): validate_candidate passed = True (its 8000-trial pure-Python refute_check found nothing lighter); circulant-GB structural pass: lightest single-block logical 171 at 400,000 trials; gf2_fast fast pass: lightest logical 44 at 1,510,000 trials (1941 s).
  • full pass (8,000,000-trial fast pass, uncapped): validate_candidate passed = True (its 8000-trial pure-Python refute_check found nothing lighter); circulant-GB structural pass: lightest single-block logical 171 at 400,000 trials; gf2_fast fast pass: lightest logical 38 at 8,000,000 trials (14299 s).

Claim: witness-backed upper bound d <= 38 (X <= 38, Z <= 38), not exact. The lightest logical did not move between the 5,000,000-trial screen stage, the 50,000,000-trial sketch pass, and the deep-kernel passes listed above.

Dead ends

  • Random weight-8 bivariate bicycle codes at n in [702, 1000]: k >= 21 in

    • 1 of 623 built codes; 29,716 draws gave 3 stage-3 survivors ([[980,28,35]] and [[784,22,28]] at the 5,000,000-trial sketch stage, not taken further).

  • Dihedral 2BGA with |a| = |b| = 4, n in [704, 1000]: 81,300 draws, k >= 21

    • in 526, none survived the first GPU stage (every one had a logical lighter than 25).

  • Cyclic GB pairs sharing more than the designed divisor (k = 100 to 496)

    • have d = 2 to 7; pairs whose offsets share a factor with m are direct sums.

  • GPU sketch bounds on high-rate codes inflate badly: pair-partition CPM

    • draws reading 22 to 24 at 20,000,000 sketch trials came out at 18 to 20 under a full-basis search. On the low-rate codes in this note the sketch and the full-basis instruments agree.

Tools

Model: Claude Fable 5.1 (Claude Code), matching provenance.model. Generators from research/kit (search.py samplers, group_algebra.py) and research/cyclic_gb.py; GPU RIS from verify/ris_gpu.cu built with nvcc for an NVIDIA A40, driven through verify/ris_gpu.py's input format; gf2_fast from verify/ for exact k, kernels, and the CPU RIS; verify/validate_candidate.py and verify/gate_changed.py for the gate. Compute: about 3.5 GPU hours for the stream that produced this code plus about 1 GPU hour of finalist passes, and about 4 CPU hours of gate runs.

Reproduction

Rebuild (H_X, H_Z) from the construction string in the code file's provenance: Cyclic (single-circulant-pair) generalized-bicycle code over Z_451 (research/cyclic_gb.py build_cyclic_gb): a(x) = 1 + x^53 + x^246 + x^313, b(x) = 1 + x^41 + x^229 + x^276; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with circ(v)[i, (i + j) mod 451] = v[j]. n = 2m = 902, k = 2 deg gcd(a, b, x^451 - 1) = 42, every check has weight 8. a and b were drawn as weight-4 multiples of a degree-21 divisor g of x^451 - 1 (g as a little-endian bit integer: 4044695).

Parity checks

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