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[[912,234,22]] d ≤
n
912
k
234
d
22
kd²/n
124.184
w
8
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 22, d_Z ≤ 22 · 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 22 · witness weight 22 (claimed upper_bound)
witness found by @jacksongquera · verify/gf2_fast via research/kit/surrogate.distance_rand_witness · found at 3×105 trials · survived 3×105 trials · 2026-10-21
witness operator (support, 22 qubits)
[30, 59, 85, 224, 229, 247, 272, 327, 352, 388, 438, 491, 500, 542, 588, 596, 700, 745, 764, 796, 820, 898]
d_Z 22 · witness weight 22 (claimed upper_bound)
witness found by @jacksongquera · verify/gf2_fast via research/kit/surrogate.distance_rand_witness · found at 3×105 trials · survived 3×105 trials · 2026-10-21
witness operator (support, 22 qubits)
[111, 115, 132, 167, 264, 269, 357, 367, 458, 476, 483, 493, 516, 535, 552, 582, 649, 654, 678, 740, 754, 829]
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 8 · H_Z 8 (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 3 · H_Z 3
trapping sets H_X (1,3)×912 (2,4)×9576 (3,5)×134064 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 912 (2,4): 9576 (3,5): 134064 (3,7): 19152
trapping sets H_Z (1,3)×912 (2,4)×9576 (3,5)×134064 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 912 (2,4): 9576 (3,5): 134064 (3,7): 19152

Construction & provenance

authors @jacksongquera
provenance submitted through the challenge
novelty novelty not audited
construction Pair-partition CPM CSS code (Okada-Kasai arXiv:2607.14091), (J,L)=(3,8), cyclic lift P=114 (Z_114), n=8P=912, k=234 (= 2P+6). H[i*P + r, l*P + ((r - E[i][l]) mod P)] = 1 for i in 0..2, l in 0..7, r in Z_P, with the 3x8 exponent arrays over Z_114: E_x = [[7, 36, 9, 74, 72, 80, 62, 78], [87, 104, 31, 0, 102, 78, 34, 74], [102, 26, 88, 102, 97, 50, 71, 12]], E_z = [[113, 58, 99, 76, 64, 82, 38, 100], [65, 5, 67, 85, 80, 49, 70, 89], [101, 72, 45, 98, 96, 46, 28, 58]]. The arrays solve the paired-difference design system E_x[i][a] - E_x[i][b] - E_z[j][a] + E_z[j][b] = 0 for each pair (a,b) of the cube 1-factorization matching M0=(0,4)(1,7)(2,6)(3,5), M1=(0,7)(1,2)(3,4)(5,6), M2=(0,2)(1,5)(3,7)(4,6); cell (i,j) uses M[(i-j) mod 3] (solution lattice of rank 19, sampled mod P); no 4- or 6-cycles in either exponent array (Tanner girth 8); the draw was moved in the solution lattice by simulated annealing (T0=64) on the number of vanishing 8-cycle exponent sums over 15000 moves without changing k. Draw seed 72114432 from anneal run 1; temperature decreased geometrically from 64 toward 4, with validated fold and connectivity checkpoints every 200 accepted moves. The method and exponent arrays are documented in notes/912-234-22.md.
model Claude Claude Fable 5.1 (claimed, not verified)
builds on arXiv:2607.14091, arXiv:quant-ph/0701020
date 2026-10-21
notes No board duplicate detected by fingerprint or WL-signature checks; no claim of general code inequivalence or literature novelty. Witness-backed upper bounds d_X <= 22 and d_Z <= 22. RIS ladder (trials per side, lightest found): 2,000: 32; 10,000: 22; 30,000: 22; 300,000: 22; 200,000 (seed 51): 22; 2,000,000 (seed 52): 22; 8,000,000 (seed 53): 22; 500,000 at pair depth 48 (seed 909): 22. The subgroup quotient filter found weight 24; a separate recorded fold search returned 152. Neither is a lower bound. The second draw at the same parameters is not submitted.
family pair-partition CPM (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

[[912,234,22]] — pair-partition CPM (3,8) code at P = 114

Direction & hypothesis

Target: the unrestricted weight-8 CSS cell. At submission preparation on 21 October 2026, codes/928-238-22.json by @MicheldeMessieres has the highest reported kd^2/n in this cell, 124.12931. This candidate gives 124.18421 using its submitted upper bound. It extends the Pareto frontier and dominates no existing entry: relative to that comparator it uses fewer physical qubits but encodes fewer logical qubits, at the same reported distance and weight. The score comparison is separate from Pareto dominance and could change if a lighter logical is found.

The comparator's note reports two P = 114, k = 234 draws reading 22 in a Stern screen without further investigation. The hypothesis here was that a longer anneal of the 8-cycle count could produce a P = 114 draw that retained that reading under deeper searches. This is evidence about a selected instance, not a demonstrated causal advantage of annealing.

Inspired by: codes/928-238-22.json and codes/976-250-22.json by @MicheldeMessieres for the even-lift k = 2P + 6 mechanism, anneal length and fold filter; codes/904-230-22.json by @vprusso for the matchings and 8-cycle polishing; codes/808-206-20.json by @pandey-tushar for the girth-8 filter; and fieldnotes/2026-09-20-screening-traps-at-n-900.md by @e-eight for the score and lift-cap discussion.

Technique: the pair-partition construction and paired-difference design system are due to Okada and Kasai (arXiv:2607.14091v4). Quasi-cyclic quantum LDPC constructions using circulant permutation matrices precede this work, including Hagiwara and Imai (arXiv:quant-ph/0701020v4). The contribution is this draw, the annealing schedule with fold checkpoints, and the distance evidence below. Literature novelty remains unverified.

What was searched

At P = 114, draw solutions of the 36 paired-difference equations in the Reproduction section using a 19-dimensional integer solution basis reduced modulo 114. Require girth 8 in both Tanner graphs and compute k over GF(2). The ordinary arms retain starting draws with k >= 234; the residue-class arm selects a mod-3 class supporting k >= 236.

For subgroup orders m = 2, 3, 6, search the quotient lift over Z_(114/m) at 1,000 RIS trials per side. Lift a quotient word to the full code and check its commutation and non-membership in the same-type stabilizer row space. Discard a draw if a valid lifted logical has weight below 22. A quotient word alone is insufficient: its lift might be a stabilizer.

For the long anneals, try 15,000 single-coefficient changes in the design basis. Reject girth violations; accept an increase delta in the summed 8-cycle count with probability exp(-delta/T), with T decreasing geometrically from 64 toward 4. Recheck the starting k after every accepted move and connectivity and the fold filter every 200 accepted moves, reverting to a validated checkpoint on failure. Return the validated state with the lowest 8-cycle count. For the submitted draw, k remains 234.

The long-anneal arms screen at 2,000 RIS trials per side, then escalate readings of at least 22 through 10,000, 30,000 and 300,000 trials on fresh seeds. The greedy control instead uses 2,000 and 30,000 trials, with deep follow-up recorded separately. Counts below are completed task records, excluding metadata, reconciled on 21 October 2026. A screened draw has a recorded full-code RIS reading after its fold filter and climb.

| Arm at P = 114 | Completed tasks | Fold-capped | Screened | Final recorded readings | |---|---:|---:|---:|---| | Greedy, 400 moves | 1,641 | 1,078 | 563 | 12: 77; 14: 20; 16: 188; 18: 128; 20: 148; 22: 2 | | Anneal, 15,000 moves, run 1 | 1,867 | 1,247 | 620 | 12: 9; 14: 20; 16: 219; 18: 130; 20: 240; 22: 2 | | Anneal, 15,000 moves, run 2 | 2,002 | 1,338 | 664 | 12: 7; 14: 22; 16: 267; 18: 96; 20: 272 | | Designed mod-3 class, 2,000 moves | 1,522 | 1,152 | 370 | 12: 23; 14: 15; 16: 186; 18: 47; 20: 99 |

Annealed readings of 22 reached 300,000 trials; greedy readings reached 30,000. These are not matched-depth success rates. Follow-up appears below. The anneal runs screened 1,284 draws.

Evidence trail

Submitted draw seed: 72114432, anneal run 1. Each row below is a fresh-seed gf2_fast random-information-set search; the reading is the lightest logical found across the X and Z sides, not two separate side-specific readings. Finds were checked for zero syndrome and exclusion from the same-type stabilizer row space. Trial budgets are per side, distributed across threads.

| Trials per side | Seed | Pair depth | Lightest found | |---:|---:|---:|---:| | 2,000 | 505801027 | 8 | 32 | | 10,000 | 506801030 | 8 | 22 | | 30,000 | 507801033 | 8 | 22 | | 300,000 | 508801036 | 8 | 22 | | 200,000 | 51 | 8 | 22 | | 2,000,000 | 52 | 8 | 22 | | 8,000,000 | 53 | 8 | 22 | | 500,000 | 909 | 48 | 22 |

The ladder budgets sum to 11,042,000 trials per side, excluding fold and packaging searches and the gate. The first reading was 32; seven later rungs found 22. Separately, the stored X and Z witnesses have weight 22 and record 300,000-trial searches with seeds 777 and 778, respectively; the latter used the sides swapped. Both witness supports and their provenance are preserved.

The campaign's subgroup quotient filter found a valid lifted logical of weight 24 for this draw. A separate recorded research/foldbound.py run returned 152 as its lightest found lifted logical. These instruments use different partitions and neither supplies a lower bound; 152 does not exclude logicals below 152 and adds no tighter bound than the stored 22.

Claim: d_X <= 22 and d_Z <= 22, with confidence upper_bound. No lower bound is claimed. The incumbent's notes/928-238-22.md reports a completed cpm_distance enumeration through weight 20 and a parity argument; that enumeration was not run here. Repeated heuristic failures to find a lighter logical do not provide the same evidence. Selecting the draw by its found upper bound also introduces a search-depth selection effect.

The final-document gate through research/kit/promote.py passed against the current board: no lighter logical in 8,000 RIS trials, seed 1437419671; no dominator, dominated entry, distance-only peer or duplicate match. Board checks and frontier membership concern this board only; absence of fingerprint or WL matches is not a general proof of code inequivalence. CI's fresh deep refutation remains outstanding, and its trial target is subject to a wall-clock budget.

A second draw, seed 72115344, has different exponent arrays and the same reported parameters. Its in-worker readings were 38, 26, 22, 22 at 2,000, 10,000, 30,000, 300,000 trials. It then found 22 at 200,000 (seed 51), 2,000,000 (seed 52), and 8,000,000 (seed 53), all at pair depth 8. Its 8M rung completed in about 5,601 seconds. It is not submitted because the same parameter point adds no frontier extension. No depth-48 result is claimed for that second draw.

Dead ends

  • Greedy control seed 60114136 fell from 22 at 30,000 trials to 20 at

    • 300,000, seed 401. A second control, seed 61114449, read 22 at 30,000; no deeper follow-up is present in the reviewed records. It cannot be counted as either a deep success or a deep failure.

  • The P = 114 mod-3 arm had 1,152 of 1,522 completed tasks fold-capped;

    • all 370 screened results were at most 20. This is about 76% fold-capped, rather than the 92% reported in an earlier draft.

  • At P = 115, the designed mod-5 arm completed 149 tasks: six fold-capped

    • and 143 screened, reading 12 in 123 cases, 16 in 19, and 18 in one. This arm produced no reading of 22.

  • Anneal run 2 produced no reading above 20 among 664 screened draws.

    • These outcomes describe the tested draws, not an impossibility result for a lift or a residue class.

Tools

Code search: Claude Fable 5.1 in Claude Code, matching provenance.model, for @jacksongquera. Python and NumPy implement the design system, anneal and quotient filter; research/kit/surrogate.py wraps the verify/gf2_fast backend; research/kit/submit.py packages witnesses. Supplementary folding uses research/foldbound.py. The campaign estimated about 45 CPU-hours for four P = 114 search arms and 12 for follow-up ladders, approximately 57 total; these are campaign estimates, not a precise cost for this selected code. The custom search orchestration is described here and is not a committed script. Evidence reconciliation and submission preparation were performed afterward in Codex; the code-search model attribution is unchanged.

Reproduction

Set P = 114 and use these exponent arrays:

E_x = [[7, 36, 9, 74, 72, 80, 62, 78],
       [87, 104, 31, 0, 102, 78, 34, 74],
       [102, 26, 88, 102, 97, 50, 71, 12]]
E_z = [[113, 58, 99, 76, 64, 82, 38, 100],
       [65, 5, 67, 85, 80, 49, 70, 89],
       [101, 72, 45, 98, 96, 46, 28, 58]]

Start with zero 342 by 912 binary matrices. For i = 0..2, j = 0..7, r = 0..113, set H_X[i*P+r, j*P+((r-E_x[i][j]) mod P)] = 1; use E_z for H_Z. Qubit j*P+c is column block j, offset c. Enumerate rows in increasing i*P+r order and sort each support to reconstruct checks.X and checks.Z in codes/912-234-22.json.

The matchings are M0 = (0,4)(1,7)(2,6)(3,5), M1 = (0,7)(1,2)(3,4)(5,6), M2 = (0,2)(1,5)(3,7)(4,6). For each pair (a,b) in M[(i-j) mod 3], the arrays obey E_x[i][a]-E_x[i][b]-E_z[j][a]+E_z[j][b] = 0 modulo 114. The two ranks are 339, so k = 912-339-339 = 234. Check weight is 8.

Run uv run python verify/qldpc_verify.py codes/912-234-22.json to check structure, commutation, rank, connectivity and the stored nontrivial weight-22 witnesses, with its local refutation pass. The exponent arrays reconstruct the submitted matrices; they do not replay the heuristic search trajectory. This two-file submission includes no automated constructor or reproduction manifest. The arrays, lift rule, seeds and budgets are recorded here. No circuit tier is included: n = 912 exceeds the tier's n <= 200 cap.

Parity checks

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