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[[762,28,32]] d ≤
n
762
k
28
d
32
kd²/n
37.627
w
7
X/Z
1.22

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Distance

X/Z asymmetry 1.22 · d_X ≤ 32, d_Z ≤ 39 · w_X = 7, w_Z = 7 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 32 · witness weight 32 (claimed upper_bound)
witness operator (support, 32 qubits)
[0, 45, 105, 179, 194, 239, 245, 254, 299, 306, 321, 359, 366, 372, 381, 437, 438, 468, 473, 498, 503, 564, 569, 581, 600, 630, 635, 692, 696, 708, 722, 752]
d_Z 39 · witness weight 39 (claimed upper_bound)
witness operator (support, 39 qubits)
[15, 38, 82, 143, 165, 188, 209, 270, 314, 315, 395, 396, 402, 410, 419, 441, 447, 455, 492, 500, 522, 524, 536, 537, 545, 546, 558, 582, 596, 627, 651, 656, 663, 672, 695, 701, 716, 723, 746]
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 7 · H_Z 7
qubit degrees H_X 3–4 (mean 3.5) · H_Z 3–4 (mean 3.5)
trapping sets H_X (1,3)×381 (2,4)×1143 (3,3)×381 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 381 (1,4): 381 (2,4): 1143 (2,5): 4572 (2,6): 2286 (3,3): 381 (3,5): 3429 (3,6): 40513 (3,7): 59817 (3,8): 20193 (3,9): 6858 (3,10): 1524
trapping sets H_Z (1,3)×381 (2,4)×1143 (3,3)×381 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 381 (1,4): 381 (2,4): 1143 (2,5): 4572 (2,6): 2286 (3,3): 381 (3,5): 3429 (3,6): 40513 (3,7): 59817 (3,8): 20193 (3,9): 6858 (3,10): 1524

Construction & provenance

authors @FarLab
provenance submitted through the challenge
novelty novelty not audited
construction Cyclic generalized-bicycle code on the ring F_2[x]/(x381 - 1) with a(x) = x47 + x113 + x332, b(x) = x46 + x68 + x113 + x300; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] (research/kit/gf2poly.cyclic_gb(381, [47, 113, 332], [46, 68, 113, 300]); circ(v)[i, (i + j) mod 381] = v[j]). k = 2 deg gcd(a, b, x381 - 1) = 28; a and b are sparse multiples of a designed divisor of x381 - 1.
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 ≤ 8 (computed)

How this code was found

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

[[762,28,32]] — weight-7 cyclic generalized-bicycle code over Z_381 (designed divisor of degree 14, trinomial-quadrinomial pair)

Direction & hypothesis

Cell: unrestricted x weight-8 (maximum check weight 7), tier n > 700, where the verifier admits a claim only with max check weight <= 8 and d <= 40. That tier is thin: at n = 701..1000 the weight <= 8 frontier had 57 points, and for mid k it is inherited from below 700 ([[576,32,20]] and [[672,20,32]] at weight 6, [[700,44,16]] at weight 7, [[708,24,24]], [[944,32,24]], [[948,24,28]]). A weight <= 7 code with k = 28 at n <= 762 advances once d >= 21. The hypothesis was that the designed-divisor cyclic GB family, which the board uses almost only at n <= 700, reaches d around 30 at k = 28 with one weight-3 and one weight-4 polynomial once m has irreducible factors of moderate degree (381 = 3 x 127; the multiplicative order of 2 is 7 mod 127 and 14 mod 381, so x^381 - 1 splits into factors of degrees 1, 2, 7 and 14, and the divisor here is one of the degree-14 factors).

What was searched

  • Designed-divisor cyclic GB over odd m in 301..499, H_X = [circ(a) | circ(b)],

    • H_Z = [circ(b)^T | circ(a)^T]: up to 40 random divisors g of x^m - 1 per m with deg g in 11..30, weight-3 and weight-4 multiples from 400 Prange rounds (research/kit/gf2poly.sparse_multiples), pairs in bands (3,4) and (4,4) with k = 2 deg gcd(a, b, x^m - 1) in 22..60 and k <= 2 deg g + 6, direct sums dropped. 1,528 pairs over 46 fertile m.

  • Screen with gf2_fast RIS (research/kit/surrogate, pair depth 8): 3,000

    • trials each; 20,000 on the 92 survivors in cells that could still advance; 300,000 on the best 18. At m = 381 the (3,4) band gave eleven k = 28 pairs, seven of which were above the bar after 20,000 trials; the best three went to 300,000.

  • Dominance against the board checkout at run time (n down, k up, d up,

    • w down; equality counts as dominated) with the n > 700 admissibility rule.

Evidence trail

The submitted pair: a(x) = x^47 + x^113 + x^332, b(x) = x^46 + x^68 + x^113 + x^300, g = gcd(a, b, x^381 - 1) of degree 14 (0x505b as a little-endian bit integer, irreducible). Row weight 7 on every check.

| instrument (gf2_fast RIS, pair depth 8) | trials per side | lightest logical | |---|---:|---:| | screen stage 1 | 3,000 | 44 | | screen stage 2 | 20,000 | 37 | | screen stage 3 | 300,000 | 33 | | gate refutation pass (verify/validate_candidate.py, seed 1219675718) | gate's own | 32 (X) | | quick fresh-seed ladder, seed 48709 | 2,000,000 | 32 (X) | | deep ladder, fresh seed 49148 | 20,000,000 | 32 (X) | | deep ladder, fresh seed 57067 | 20,000,000 | 32 (X) | | qldpc submit fast pass (packaging) | 10,000,000 | nothing lighter |

The d = 33 document was staged first; the gate refuted it with a weight-32 X logical, the same weight the independent 2,000,000-trial run found, and the document was re-staged at d = 32 with that witness before the deep ladder. Two 20,000,000-trial runs on fresh seeds and the packaging pass found nothing below 32; a third 20,000,000-trial run was still going when this note was written, and the submission was filed only after it finished without finding a lighter logical. Claim: witness-backed upper bound d <= 32, not exact. The code advances the board for any d >= 21, so the margin over the bar is large even if a later sweep tightens the bound.

Near misses: the other two k = 28 pairs at m = 381 sit at d <= 28 after 300,000 trials ([1, 19, 253] / [145, 272, 285, 297] and [185, 236, 308] / [43, 71, 149, 297]); not submitted, same cell, lower bound.

Dead ends

  • Weight-(3,3) trinomial pairs, exhaustive over m = 351..500 with k >= 18:

    • the only cells were k = 18 (m = 365, 381, 438, 465), 20 (372, 465), 22 (438), 24 (420), 28 (381), 30 (434), 36 (438), 40 (465); everything with k >= 20 was at d <= 24 after 1,000 trials (the k = 28 trinomial pairs at m = 381 have d <= 2: a = 1 + x^127 + x^254 type words); the k = 18 cells (bar d >= 33 from [[672,20,32]]) gave the separately filed weight-6 [[930,18,36]].

  • (4,4) pairs at the same m = 381: k = 34 only, all d <= 3 at 3,000 trials.
  • n > 720 with k = 36..62 at w = 8 (m = 385, 399, 403, 429, 455, 475, 483, 495):

    • d <= 5..20 at 3,000 trials against bars of 21..23; one [[910,46,35]] at 1,000 trials fell to 25 at 3,000 and below the bar after 20,000.

  • BB and metacyclic 2BGA samplers with random supports were prepared but not

    • run for lack of box time; the designed-divisor route produced every survivor.

Tools

Claude Fable 5.1 (provenance.model) ran the search on a Brev n2d-highcpu-64 box; the 20,000,000-trial ladders and packaging were finished by Claude Opus 5.5 after a model switch. gf2_fast (verify/gf2_fast) through research/kit/surrogate with 20 threads per ladder; research/kit/gf2poly for factoring, divisors, Prange sparse multiples and the circulant builder; research/kit/prescreen for the direct-sum check; research/kit/submit for packaging; verify/validate_candidate.py as the gate. About 25 CPU-hours of screening shared with the other codes of this sweep and about 40 CPU-hours of ladders for this code.

Reproduction

import sys; sys.path[:0] = ["research/kit", "verify"]
import gf2poly
HX, HZ = gf2poly.cyclic_gb(381, [47, 113, 332], [46, 68, 113, 300])
assert gf2poly.designed_k(381, [47, 113, 332], [46, 68, 113, 300]) == 28

circ(v)[i, (i + j) mod 381] = v[j]; qubits 0..380 form the left block and 381..761 the right block. Unit multiples of the exponents mod 381, common shifts, and swapping a with b give the same code up to qubit permutation. Literature novelty unverified; board-relative novelty from verify/validate_candidate.py.

Parity checks

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