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[[808,206,20]] d ≤
n
808
k
206
d
20
kd²/n
101.98
w
8
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 20, d_Z ≤ 20 · 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 20 · witness weight 20 (claimed upper_bound)
witness operator (support, 20 qubits)
[54, 81, 85, 93, 186, 241, 277, 330, 392, 420, 456, 482, 486, 508, 577, 596, 632, 659, 747, 771]
d_Z 20 · witness weight 20 (claimed upper_bound)
witness operator (support, 20 qubits)
[25, 48, 57, 97, 221, 270, 299, 303, 332, 391, 449, 478, 481, 494, 576, 585, 598, 626, 675, 704]
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)×808 (2,4)×8484 (3,5)×118776 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 808 (2,4): 8484 (3,5): 118776 (3,7): 16968
trapping sets H_Z (1,3)×808 (2,4)×8484 (3,5)×118776 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 808 (2,4): 8484 (3,5): 118776 (3,7): 16968

Construction & provenance

authors @pandey-tushar
provenance submitted through the challenge
novelty novelty not audited
construction Pair-partition CPM CSS code (Okada-Kasai arXiv:2607.14091), (J,L)=(3,8), prime lift P=101, n=8P=808, k=2P+4=206. H[i*P + r, j*P + ((r - E[i][j]) mod P)] = 1 with 3x8 exponent arrays over Z_101: E_x = [[37, 25, 46, 33, 40, 50, 97, 26], [61, 87, 90, 30, 63, 60, 39, 75], [56, 59, 72, 97, 7, 33, 71, 40]], E_z = [[88, 0, 3, 58, 91, 75, 54, 1], [78, 74, 87, 69, 80, 99, 36, 62], [80, 88, 8, 24, 31, 61, 7, 69]]. The arrays solve the joint design system E_x[i][j] - E_x[i][j'] - E_z[i'][j] + E_z[i'][j'] = 0 for each column pair {j,j'} of the matching M[(i-i') mod 3], 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); girth 8 (no 4- or 6-cycles in either exponent array).
model Claude Claude Opus 5 (claimed, not verified)
builds on arXiv:2607.14091
date 2026-09-18
notes Same pair-partition CPM construction as the board's [[584,150,18]] (P=73, published), [[632,162,18]] (P=79) and [[664,170,18]] (P=83), at prime lift P=101 (n=808), which the n<=1000 / w<=8 / d<=40 blocklength rule admits. Distance is a witness-backed upper bound: accelerated RIS ladder 2k, 20k, 200k and 1M trials all at 20. The trusted candidate gate reported no exact duplicate and no WL-equivalent board entry. Literature novelty of these parameters is unverified.
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

[[808,206,20]] — pair-partition CPM code at prime lift P = 101

Direction & hypothesis

Target: the highest kd^2/n inside the hackathon box (n <= 1000, w <= 8, d <= 40). The weight-8 leaders are all one published family, pair-partition CPM CSS codes (Okada-Kasai, arXiv:2607.14091) with (J,L) = (3,8), n = 8P and k = 2P + 4: [[584,150,18]] (P = 73), [[632,162,18]] (P = 79) and [[664,170,18]] (P = 83), all near kd^2/n = 83.

Two observations set the target. First, k = 2P + 4 makes kd^2/n = d^2/4 plus a small term, so the score depends almost only on d; d = 18 at a larger lift does not help (P = 89 gives 82.8). Second, those entries were made under the old n <= 700 cap (P <= 87). The current rule admits n <= 1000 for w <= 8 and d <= 40, so primes P = 89 to 113 were open. The hypothesis was that the distance keeps growing with the lift, as it did from P = 23 (d = 10) to P = 73 (d = 18), and that d = 20 is reachable.

Ceiling: these codes have column weight 3 built from circulant permutation matrices, so the classical distance of the check matrix kernel is at most (J+1)! = 24, which caps the family near kd^2/n = 145.

What was searched

The construction follows the recipe in notes/632-162-18.md: fixed matchings 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), and the joint design system

E_x[i][j] - E_x[i][j'] - E_z[i'][j] + E_z[i'][j'] = 0 (mod P)

for each column pair {j,j'} of M[(i - i') mod 3]: 36 equations in 48 unknowns, null space of dimension 19 over Z_P. Candidates are uniform random vectors of that null space.

Control: at P = 29 and P = 79 the rebuilt system has nullity 19, satisfies CSS commutation and gives k = 2P + 4 exactly. At P = 79, 28 random valid draws screened at 2,000 trials reached d = 18, the published value, and the girth-8 draws scored highest, so girth 8 was made a hard filter.

Sweep: P in {89, 97, 101, 103, 107, 109, 113}, roughly 15,000 draws, stopped at a fixed wall-clock budget. Filters in order: no 4- or 6-cycles in either exponent array, CSS, k = 2P + 4, connected Tanner graph. 1,528 draws survived. Each was screened with the accelerated RIS search at 2,000 trials, and anything at 19 or more was rescreened at 20,000. Distance below is the minimum over both rungs:

P valid d = 20 d = 22 89 156 0 0 97 194 1 0 101 224 9 0 103 240 13 0 107 203 19 0 109 257 39 1 113 254 36 1

Everything else read 18 or less.

Evidence trail

Submitted code, P = 101 (accelerated RIS, both sides, lightest logical):

2,000 trials 20 20,000 trials 20 200,000 trials 20 1,000,000 trials 20

A second code, [[856,218,20]] at P = 107, was flat at 20 through the same ladder. The final witnesses have weight 20 on both sides. X came from the accelerator (eight seeds at 200,000 trials, all weight 20), and Z from the kit's lightest_logical. Both were checked in the kernel and outside the row space by the Python GF(2) stack. verify/validate_candidate.py passed with refutation on (seed 1156134637): no lighter logical, no exact duplicate, no WL-equivalent board entry, board-advancing in the weight-8 cell.

The claim is a witness-backed upper bound d <= 20, not an exact distance.

Dead ends

  • Shallow readings inflate heavily at this size. Draws read 26 to 44 at 2,000

    • trials and fell to 18 or 20 at 20,000.

  • The two d = 22 draws (P = 109, 113) both fell to 20 at 200,000 trials. No

    • d = 22 survived, so d = 20 looks like the plateau for P <= 113 at this sampling depth.

  • d = 18 at a larger lift lowers the score, since kd^2/n = 100 + 200/P at

    • d = 20 and 81 + 162/P at d = 18. Smaller P is better at fixed d.

Tools

Claude Opus 5 in Claude Code (desktop app) on a 16-core Windows machine. Repo tooling: research/kit (css.py, surrogate.py, submit.py), verify/validate_candidate.py, and the gf2_fast accelerator built with MSVC. About 2.5 hours of sweep and 2 hours of deep ladders.

Reproduction

import numpy as np P = 101 Ex = [[37, 25, 46, 33, 40, 50, 97, 26], [61, 87, 90, 30, 63, 60, 39, 75], [56, 59, 72, 97, 7, 33, 71, 40]] Ez = [[88, 0, 3, 58, 91, 75, 54, 1], [78, 74, 87, 69, 80, 99, 36, 62], [80, 88, 8, 24, 31, 61, 7, 69]]

def build(E): H = np.zeros((3 * P, 8 * P), dtype=np.int8) r = np.arange(P) for i in range(3): for j in range(8): H[i * P + r, j * P + (r - E[i][j]) % P] = 1 return H

HX, HZ = build(Ex), build(Ez) # n = 808, k = 206

Parity checks

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