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[[899,18,31]] d ≤
n
899
k
18
d
31
kd²/n
19.241
w
8
X/Z
1
g
0.0594
r
4.2426
layers
2
swaps
3129

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Distance

X/Z asymmetry 1 · d_X ≤ 31, d_Z ≤ 31 · 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 31 · witness weight 31 (claimed upper_bound)
witness found by @dorakingx · Clifford witness transform · found at 2×107 trials · survived 2×107 trials · 2026-09-17
witness operator (support, 31 qubits)
[22, 34, 333, 356, 375, 400, 416, 418, 436, 438, 453, 464, 465, 478, 506, 523, 540, 569, 586, 606, 609, 612, 632, 655, 672, 698, 717, 737, 740, 783, 803]
d_Z 31 · witness weight 31 (claimed upper_bound)
witness found by @vprusso · Clifford witness transform · found at 3×108 trials · survived 3×108 trials · 2026-09-25
witness operator (support, 31 qubits)
[101, 164, 184, 204, 210, 224, 227, 244, 250, 256, 267, 273, 279, 304, 307, 310, 313, 316, 319, 322, 324, 345, 641, 666, 691, 709, 730, 732, 753, 774, 795]
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 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 2–8 (mean 7.107) · H_Z 2–8 (mean 7.075)
qubit degrees H_X 1–6 (mean 3.605) · H_Z 1–4 (mean 3.463)
trapping sets H_X (1,1)×59 (2,0)×4 (3,0)×49 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 59 (1,2): 111 (1,3): 65 (1,4): 568 (1,5): 83 (1,6): 13 (2,0): 4 (2,1): 135 (2,2): 191 (2,3): 495 (2,4): 838 (2,5): 732 (2,6): 6564 (2,7): 827 (2,8): 333 (2,9): 152 (2,10): 12 (3,0): 49 (3,1): 173 (3,2): 627 (3,3): 2212 (3,4): 3797 (3,5): 8127 (3,6): 17586 (3,7): 14341 (3,8): 106865 (3,9): 15747 (3,10): 18020 (3,11): 4440 (3,12): 2378 (3,13): 516 (3,14): 50
trapping sets H_Z (1,1)×55 (2,0)×15 (3,0)×21 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 55 (1,2): 125 (1,3): 68 (1,4): 651 (2,0): 15 (2,1): 127 (2,2): 269 (2,3): 443 (2,4): 920 (2,5): 776 (2,6): 7585 (3,0): 21 (3,1): 233 (3,2): 774 (3,3): 2017 (3,4): 4376 (3,5): 8176 (3,6): 19812 (3,7): 14544 (3,8): 125243 (3,9): 1312 (3,10): 13730
witness diameter X 23.3238 · Z 23.7065 (Euclidean support diameter of the stored distance witnesses in the layout; an upper bound on the exhibited logicals’ spread, not a minimum over all logicals)

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 4.243
X checkZ checkqubit site (454)2 qubits stacked (2 layers)dashed: the pair setting the interaction radiushover a check to isolate its qubits; click to pin — repeated clicks cycle through overlapping checks; click empty space to release
routing cost 3129 nearest-neighbor SWAPs per round in total, at most 5 for one check (heuristic: MST lower bound on the layout, with one lattice step = the minimum qubit spacing 1; not a rank)

Construction & provenance

authors @dorakingx and @DennisWayo
provenance submitted through the challenge
novelty new parameter set claimed by submitter
construction Recursive 25-qubit Clifford/stabilizer-row-space reduction of codes/924-18-31.json, continuing through the merged codes/920-18-31.json parent. At each one-qubit step, a low-weight row-space stabilizer S is substituted into a generating set, its selected qubit is cleared from the remaining same-type checks, a CNOT fan-out disentangles that qubit, and the qubit is deleted. The 21 new steps below codes/920-18-31.json were generated by enumerating connected sums of at most three checks, accepting only candidates that preserve k=18, maximum check weight 8, the inherited local-2d-bilayer layout, and interaction radius 4.242640687119285. Both logical witnesses were transformed through every Clifford step and remain valid at weight 31. This preserves a witness-backed upper bound only; it does not certify the minimum distance.
model GPT-5 (Codex) (claimed, not verified)
builds on arXiv:2504.08887
date 2026-10-15
notes Recursive derivative of merged codes/920-18-31.json, not an independent construction. The original codes/924-18-31.json construction is credited to @e-eight. The merged parent reductions are credited to @dorakingx with Claude Opus 5 (Claude Code), and the codes/920-18-31.json contribution and this 21-step continuation to [[899,18,d<=31]] are credited to @DennisWayo with GPT-5 (Codex). The new chain preserves k=18, maximum check weight 8, local-2d-bilayer geometry, interaction radius 4.242640687119285, and transformed X/Z logical witnesses of weight 31 while deleting 21 additional physical qubits. Two independent CI-style fire passes used seeds 2026101501 and 2027101504. Each pass ran the structural detector, 132880 ordinary RIS trials, and 8000000 RIS-fast trials. Neither pass found a logical below weight 31; RIS-fast reached weight 31 in both passes. The combined post-reduction attack budget was 265760 ordinary RIS trials plus 16000000 RIS-fast trials. Distance remains an upper bound, not an exact claim, and literature novelty is unverified. Reduction trace from [[920,18,d<=31]] to [[899,18,d<=31]]: Derived by a one-qubit Clifford reduction on X-type row-space stabilizer support [0, 465], removing source qubit 0. The row-space element used source rows [341]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on X-type row-space stabilizer support [456, 459, 917], removing source qubit 459. The row-space element used source rows [466]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on X-type row-space stabilizer support [20, 459, 464, 482], removing source qubit 459. The row-space element used source rows [375, 2, 357]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on X-type row-space stabilizer support [0, 463], removing source qubit 0. The row-space element used source rows [341]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on X-type row-space stabilizer support [20, 458, 463, 481], removing source qubit 458. The row-space element used source rows [341, 356]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on X-type row-space stabilizer support [433, 436, 891, 914], removing source qubit 436. The row-space element used source rows [443]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on X-type row-space stabilizer support [21, 41, 458, 476, 500], removing source qubit 476. The row-space element used source rows [387]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on Z-type row-space stabilizer support [20, 519], removing source qubit 20. The row-space element used source rows [360]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on Z-type row-space stabilizer support [19, 517], removing source qubit 19. The row-space element used source rows [342]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on Z-type row-space stabilizer support [19, 61, 455, 518], removing source qubit 455. The row-space element used source rows [376]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on Z-type row-space stabilizer support [393, 434, 824, 844, 890], removing source qubit 434. The row-space element used source rows [392]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on X-type row-space stabilizer support [436, 889], removing source qubit 889. The row-space element used source rows [442]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on Z-type row-space stabilizer support [17, 59, 82, 491, 534], removing source qubit 17. The row-space element used source rows [392]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on X-type row-space stabilizer support [408, 411, 452, 862, 885, 903], removing source qubit 411. The row-space element used source rows [423]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on X-type row-space stabilizer support [448, 451, 903], removing source qubit 451. The row-space element used source rows [457]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on Z-type row-space stabilizer support [367, 883], removing source qubit 883. The row-space element used source rows [443]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on Z-type row-space stabilizer support [389, 903], removing source qubit 903. The row-space element used source rows [443]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on Z-type row-space stabilizer support [17, 59, 532], removing source qubit 17. The row-space element used source rows [427]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on X-type row-space stabilizer support [33, 465, 487], removing source qubit 487. The row-space element used source rows [371]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on Z-type row-space stabilizer support [387, 430, 859, 900], removing source qubit 430. The row-space element used source rows [408]. Distance remains a witness-backed upper bound. Derived by a one-qubit Clifford reduction on Z-type row-space stabilizer support [16, 56, 79, 485, 527], removing source qubit 16. The row-space element used source rows [408]. Distance remains a witness-backed upper bound.
family tile (a tag, not a ranking)
locality 2D-local bilayer (computed from the layout)
weight class weight ≤ 8 (computed)

How this code was found

no research note was staged with this submission — notes are requested for new submissions (notes/README.md)

Parity checks

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