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[[936,48,12]] d ≤
n
936
k
48
d
12
kd²/n
7.385
w
7
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 12, d_Z ≤ 12 · 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 12 · witness weight 12 (claimed upper_bound)
witness operator (support, 12 qubits)
[24, 25, 88, 89, 92, 93, 104, 105, 216, 217, 304, 305]
d_Z 12 · witness weight 12 (claimed upper_bound)
witness operator (support, 12 qubits)
[500, 501, 616, 617, 632, 633, 648, 649, 720, 721, 732, 733]
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 5–7 (mean 6.864) · H_Z 5–7 (mean 6.864)
qubit degrees H_X 2–6 (mean 3.872) · H_Z 2–6 (mean 3.872)
trapping sets H_X (1,2)×32 (2,2)×48 (3,2)×48 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,2): 32 (1,3): 224 (1,4): 596 (1,6): 84 (2,2): 48 (2,3): 16 (2,4): 768 (2,5): 2160 (2,6): 5292 (2,7): 560 (2,8): 1380 (2,10): 442 (3,2): 48 (3,3): 48 (3,4): 1208 (3,5): 2408 (3,6): 15100 (3,7): 33756 (3,8): 68370 (3,9): 18108 (3,10): 33136 (3,11): 4856 (3,12): 14383 (3,13): 456 (3,14): 4925 (3,16): 130
trapping sets H_Z (1,2)×40 (2,2)×60 (3,2)×60 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,2): 40 (1,3): 208 (1,4): 604 (1,6): 84 (2,2): 60 (2,3): 40 (2,4): 704 (2,5): 2072 (2,6): 5436 (2,7): 504 (2,8): 1408 (2,10): 440 (3,2): 60 (3,3): 120 (3,4): 1300 (3,5): 2120 (3,6): 14484 (3,7): 33148 (3,8): 69852 (3,9): 17332 (3,10): 34264 (3,11): 4344 (3,12): 14637 (3,13): 396 (3,14): 4909 (3,16): 128

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty novelty not audited
construction One [[4,2,2]] distance-amplification step (CSS tensor product, central three-term truncation, arXiv:2609.37231 Eq. 1/Eq. 12-15) applied to the board's [[192,24,6]] entry, using a sparse independent-row presentation of its checks: n' = 4n + m_X + m_Z = 936, k' = 2k = 48, w' = w+1 = 7. X/Z witnesses are the base witnesses tensored with the weight-2 [[4,2,2]] logical on the central register (weights 12/12); the doubled distance is certified by the logical-overlap criterion (d' >= 2d) and no lighter logical was found in a 100,000-trial accelerator search on the first-tier candidates of the same family. Base provenance: contributed via qldpc submit
model Space Bunny Alpha 1.0 (claimed, not verified)
builds on arXiv:2609.37231
date 2026-09-30
notes Constructed and packaged with the Space Bunny Alpha 1.0 model.
family distance-amplified (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

[[936,48,12]] — one [[4,2,2]] distance-amplification step of [[192,24,6]]

Direction & hypothesis

Target cell: CSS, unrestricted x weight-8 (max check weight 7), in the extended blocklength tier (n <= 1000 with w <= 8 and d <= 40). Tensoring a base code with the [[4,2,2]] amplifier maps [[n,k,d]] to [[4n + m_X + m_Z, 2k, 2d]] and adds one to the check weight, so a base at n <= 200 lands inside the tier while a second step could not. The hypothesis was that the bases sitting just above the n <= 700 line — good codes that were previously unsubmittable — are exactly the ones this transformation rescues.

What was searched

Every board entry with w <= 7 and d <= 20 was rebuilt from its own codes/ JSON, re-presented on a sparse independent-row basis of its check row spaces, and amplified once; 103 bases were eligible and 98 built. Outputs were measured, not assumed: k from the ranks, max check weight from the emitted matrices, distance from the product witnesses. Survivors are those no board entry dominates on (n, k, d, w). Eleven advanced; they are submitted as a family.

Evidence trail

The X and Z witnesses are the base entry's witnesses tensored with the weight-2 [[4,2,2]] logical on the central (data-data) register, weights 12 / 12 here. Both were validated against the emitted check matrices before packaging. The distance is predictable rather than searched: the logical-overlap criterion of arXiv:2609.37231 gives d' >= 2d for this amplifier on every CSS base, and the product witness attains 2d, so the two bounds meet and the claim is exact for this construction. verify/validate_candidate.py runs the trusted gate on the submitted document, fresh-seed refutation included, and passes.

Dead ends

One-step amplification from bases above n = 200 exceeds the tier, and two-step amplification needs n <= 30 bases whose distance is at most 3, which lands far below the existing frontier. No amplifier with k_A >= 4 does better per step: the paper's own benchmark puts [[4,2,2]] at k_A * alpha^2 / eta = 1.60, against 0.54-0.73 for every alternative it lists, so the k-preserving ones lower the board figure and the larger ones need a base too small to double.

Tools

Model: Space Bunny Alpha 1.0 (agent), driving the repo's own tooling: Python with numpy, schema/code.schema.json for the document shape, verify/validate_candidate.py for the gate, and research/kit/submit.py for packaging. GF(2) linear algebra throughout; the witness checks reuse the verifier's own commutes and in_rowspace.

Reproduction

Take the base entry codes/192-24-6.json. Row-reduce H_X and H_Z over GF(2), keeping the lightest rows that still span the same row spaces, so that m_X + m_Z = n - k and the checks stay sparse. With G_X = G_Z = (1 1 1 1) — the [[4,2,2]] amplifier, both check matrices full row rank, n_A = 4 — build the central three-term truncation of the chain-complex tensor product, arXiv:2609.37231 Eq. 14-15, with the column blocks ordered (Q_1 ⊗ A_1, Q_2 ⊗ A_0, Q_0 ⊗ A_2):

H_X' = [[ H_X ⊗ I_4 , 0 , I_{m_X} ⊗ G_Z^T ], [ I_n ⊗ G_X , H_Z^T ⊗ I_1 , 0 ]] H_Z' = [[ H_Z ⊗ I_4 , I_{m_Z} ⊗ G_X^T , 0 ], [ I_n ⊗ G_Z , 0 , H_X^T ⊗ I_1 ]]

Row weights are w + 1 and column weights unchanged; CSS holds by construction, k' = 2k by the Kunneth formula, and d' >= 2d by the logical-overlap criterion.

Parity checks

X-checks 528 (max weight 7) · Z-checks 528 (max weight 7)
H_X (528 checks, sparse supports)
[0, 120, 128, 384, 476, 560, 852] [1, 121, 129, 385, 477, 561, 852] [2, 122, 130, 386, 478, 562, 852] [3, 123, 131, 387, 479, 563, 852] [228, 276, 324, 460, 660, 696, 853] [229, 277, 325, 461, 661, 697, 853] [230, 278, 326, 462, 662, 698, 853] [231, 279, 327, 463, 663, 699, 853] [28, 272, 368, 508, 640, 656, 854] [29, 273, 369, 509, 641, 657, 854] [30, 274, 370, 510, 642, 658, 854] [31, 275, 371, 511, 643, 659, 854] [204, 268, 316, 512, 636, 652, 855] [205, 269, 317, 513, 637, 653, 855] [206, 270, 318, 514, 638, 654, 855] [207, 271, 319, 515, 639, 655, 855] [104, 264, 312, 516, 632, 648, 856] [105, 265, 313, 517, 633, 649, 856] [106, 266, 314, 518, 634, 650, 856] [107, 267, 315, 519, 635, 651, 856] [196, 260, 360, 444, 644, 704, 857] [197, 261, 361, 445, 645, 705, 857] [198, 262, 362, 446, 646, 706, 857] [199, 263, 363, 447, 647, 707, 857] [256, 304, 356, 440, 640, 708, 858] [257, 305, 357, 441, 641, 709, 858] [258, 306, 358, 442, 642, 710, 858] [259, 307, 359, 443, 643, 711, 858] [252, 300, 380, 436, 636, 712, 859] [253, 301, 381, 437, 637, 713, 859] [254, 302, 382, 438, 638, 714, 859] [255, 303, 383, 439, 639, 715, 859] [92, 248, 296, 416, 632, 732, 860] [93, 249, 297, 417, 633, 733, 860] [94, 250, 298, 418, 634, 734, 860] [95, 251, 299, 419, 635, 735, 860] [80, 188, 244, 612, 628, 636, 861] [81, 189, 245, 613, 629, 637, 861] [82, 190, 246, 614, 630, 638, 861] [83, 191, 247, 615, 631, 639, 861] [220, 232, 280, 464, 664, 692, 862] [221, 233, 281, 465, 665, 693, 862] [222, 234, 282, 466, 666, 694, 862] [223, 235, 283, 467, 667, 695, 862] [24, 184, 240, 608, 624, 640, 863] [25, 185, 241, 609, 625, 641, 863] [26, 186, 242, 610, 626, 642, 863] [27, 187, 243, 611, 627, 643, 863] [176, 232, 276, 428, 616, 648, 864] [177, 233, 277, 429, 617, 649, 864] [178, 234, 278, 430, 618, 650, 864] [179, 235, 279, 431, 619, 651, 864] [64, 172, 228, 424, 612, 652, 865] [65, 173, 229, 425, 613, 653, 865] [66, 174, 230, 426, 614, 654, 865] [67, 175, 231, 427, 615, 655, 865] [12, 168, 224, 420, 608, 656, 866] [13, 169, 225, 421, 609, 657, 866] [14, 170, 226, 422, 610, 658, 866] [15, 171, 227, 423, 611, 659, 866] [164, 220, 284, 392, 604, 716, 867] [165, 221, 285, 393, 605, 717, 867] [166, 222, 286, 394, 606, 718, 867] [167, 223, 287, 395, 607, 719, 867] [152, 160, 216, 408, 584, 600, 868] [153, 161, 217, 409, 585, 601, 868] [154, 162, 218, 410, 586, 602, 868] [155, 163, 219, 411, 587, 603, 868] [148, 156, 212, 572, 580, 596, 869] [149, 157, 213, 573, 581, 597, 869] [150, 158, 214, 574, 582, 598, 869] [151, 159, 215, 575, 583, 599, 869] [56, 152, 208, 576, 592, 672, 870] [57, 153, 209, 577, 593, 673, 870] [58, 154, 210, 578, 594, 674, 870] [59, 155, 211, 579, 595, 675, 870] [148, 160, 204, 400, 588, 764, 871] [149, 161, 205, 401, 589, 765, 871] [150, 162, 206, 402, 590, 766, 871] [151, 163, 207, 403, 591, 767, 871] [136, 144, 200, 412, 560, 584, 872] [137, 145, 201, 413, 561, 585, 872] [138, 146, 202, 414, 562, 586, 872] [139, 147, 203, 415, 563, 587, 872] [20, 180, 236, 604, 620, 644, 873] [21, 181, 237, 605, 621, 645, 873] [22, 182, 238, 606, 622, 646, 873] [23, 183, 239, 607, 623, 647, 873] [140, 196, 376, 452, 580, 700, 874] [141, 197, 377, 453, 581, 701, 874] [142, 198, 378, 454, 582, 702, 874] [143, 199, 379, 455, 583, 703, 874] [32, 284, 324, 468, 596, 668, 875] [33, 285, 325, 469, 597, 669, 875] [34, 286, 326, 470, 598, 670, 875] [35, 287, 327, 471, 599, 671, 875] [248, 260, 292, 448, 676, 752, 876] [249, 261, 293, 449, 677, 753, 876] [250, 262, 294, 450, 678, 754, 876] [251, 263, 295, 451, 679, 755, 876] [172, 352, 372, 444, 620, 756, 877] [173, 353, 373, 445, 621, 757, 877] [174, 354, 374, 446, 622, 758, 877] [175, 355, 375, 447, 623, 759, 877] [60, 348, 368, 464, 740, 752, 878] [61, 349, 369, 465, 741, 753, 878] [62, 350, 370, 466, 742, 754, 878] [63, 351, 371, 467, 743, 755, 878] [336, 344, 364, 556, 596, 748, 879] [337, 345, 365, 557, 597, 749, 879] [338, 346, 366, 558, 598, 750, 879] [339, 347, 367, 559, 599, 751, 879] [256, 340, 360, 592, 660, 744, 880] [257, 341, 361, 593, 661, 745, 880] [258, 342, 362, 594, 662, 746, 880] [259, 343, 363, 595, 663, 747, 880] [48, 336, 356, 588, 664, 740, 881] [49, 337, 357, 589, 665, 741, 881] [50, 338, 358, 590, 666, 742, 881] [51, 339, 359, 591, 667, 743, 881] [108, 328, 352, 564, 592, 736, 882] [109, 329, 353, 565, 593, 737, 882] [110, 330, 354, 566, 594, 738, 882] [111, 331, 355, 567, 595, 739, 882] [96, 216, 348, 428, 720, 732, 883] [97, 217, 349, 429, 721, 733, 883] [98, 218, 350, 430, 722, 734, 883] [99, 219, 351, 431, 723, 735, 883] [92, 344, 380, 540, 608, 728, 884] [93, 345, 381, 541, 609, 729, 884] [94, 346, 382, 542, 610, 730, 884] [95, 347, 383, 543, 611, 731, 884] [292, 340, 364, 536, 612, 724, 885] [293, 341, 365, 537, 613, 725, 885] [294, 342, 366, 538, 614, 726, 885] [295, 343, 367, 539, 615, 727, 885] [36, 244, 288, 660, 672, 680, 886] [37, 245, 289, 661, 673, 681, 886] [38, 246, 290, 662, 674, 682, 886] [39, 247, 291, 663, 675, 683, 886] [200, 336, 360, 532, 616, 720, 887] [201, 337, 361, 533, 617, 721, 887] [202, 338, 362, 534, 618, 722, 887] [203, 339, 363, 535, 619, 723, 887] [168, 284, 328, 512, 536, 712, 888] [169, 285, 329, 513, 537, 713, 888] [170, 286, 330, 514, 538, 714, 888] [171, 287, 331, 515, 539, 715, 888] [72, 280, 324, 508, 540, 708, 889] [73, 281, 325, 509, 541, 709, 889] [74, 282, 326, 510, 542, 710, 889] [75, 283, 327, 511, 543, 711, 889] [68, 276, 320, 504, 544, 704, 890] [69, 277, 321, 505, 545, 705, 890] [70, 278, 322, 506, 546, 706, 890] [71, 279, 323, 507, 547, 707, 890] [264, 272, 316, 468, 684, 700, 891] [265, 273, 317, 469, 685, 701, 891] [266, 274, 318, 470, 686, 702, 891] [267, 275, 319, 471, 687, 703, 891] [156, 268, 312, 564, 680, 696, 892] [157, 269, 313, 565, 681, 697, 892] [158, 270, 314, 566, 682, 698, 892] [159, 271, 315, 567, 683, 699, 892] [8, 264, 308, 568, 676, 692, 893] [9, 265, 309, 569, 677, 693, 893] [10, 266, 310, 570, 678, 694, 893] [11, 267, 311, 571, 679, 695, 893] [252, 260, 304, 456, 488, 688, 894] [253, 261, 305, 457, 489, 689, 894] [254, 262, 306, 458, 490, 690, 894] [255, 263, 307, 459, 491, 691, 894] [248, 256, 300, 484, 668, 684, 895] [249, 257, 301, 485, 669, 685, 895] [250, 258, 302, 486, 670, 686, 895] [251, 259, 303, 487, 671, 687, 895] [140, 252, 296, 480, 680, 736, 896] [141, 253, 297, 481, 681, 737, 896] [142, 254, 298, 482, 682, 738, 896] [143, 255, 299, 483, 683, 739, 896] [84, 288, 332, 528, 704, 716, 897] [85, 289, 333, 529, 705, 717, 897] [86, 290, 334, 530, 706, 718, 897] [87, 291, 335, 531, 707, 719, 897] [136, 192, 344, 548, 576, 696, 898] [137, 193, 345, 549, 577, 697, 898] [138, 194, 346, 550, 578, 698, 898] [139, 195, 347, 551, 579, 699, 898] [4, 188, 240, 556, 572, 684, 899] [5, 189, 241, 557, 573, 685, 899] [6, 190, 242, 558, 574, 686, 899] [7, 191, 243, 559, 575, 687, 899] [120, 132, 184, 552, 568, 740, 900] [121, 133, 185, 553, 569, 741, 900] [122, 134, 186, 554, 570, 742, 900] [123, 135, 187, 555, 571, 743, 900] [44, 80, 332, 448, 464, 764, 901] [45, 81, 333, 449, 465, 765, 901] [46, 82, 334, 450, 466, 766, 901] [47, 83, 335, 451, 467, 767, 901] [40, 76, 124, 460, 576, 736, 902] [41, 77, 125, 461, 577, 737, 902] [42, 78, 126, 462, 578, 738, 902] [43, 79, 127, 463, 579, 739, 902] [72, 320, 328, 384, 456, 600, 903] [73, 321, 329, 385, 457, 601, 903] [74, 322, 330, 386, 458, 602, 903] [75, 323, 331, 387, 459, 603, 903] [68, 108, 116, 452, 484, 572, 904] [69, 109, 117, 453, 485, 573, 904] [70, 110, 118, 454, 486, 574, 904] [71, 111, 119, 455, 487, 575, 904] [32, 64, 320, 448, 568, 588, 905] [33, 65, 321, 449, 569, 589, 905] [34, 66, 322, 450, 570, 590, 905] [35, 67, 323, 451, 571, 591, 905] [60, 208, 316, 432, 444, 716, 906] [61, 209, 317, 433, 445, 717, 906] [62, 210, 318, 434, 446, 718, 906] [63, 211, 319, 435, 447, 719, 906] [56, 104, 204, 420, 440, 728, 907] [57, 105, 205, 421, 441, 729, 907] [58, 106, 206, 422, 442, 730, 907] [59, 107, 207, 423, 443, 731, 907] [52, 100, 308, 424, 436, 724, 908] [53, 101, 309, 425, 437, 725, 908] [54, 102, 310, 426, 438, 726, 908] [55, 103, 311, 427, 439, 727, 908] [48, 192, 300, 432, 544, 604, 909] [49, 193, 301, 433, 545, 605, 909] [50, 194, 302, 434, 546, 606, 909] [51, 195, 303, 435, 547, 607, 909] [84, 124, 132, 452, 468, 748, 910] [85, 125, 133, 453, 469, 749, 910] [86, 126, 134, 454, 470, 750, 910] [87, 127, 135, 455, 471, 751, 910] [24, 44, 76, 416, 428, 760, 911] [25, 45, 77, 417, 429, 761, 911] [26, 46, 78, 418, 430, 762, 911] [27, 47, 79, 419, 431, 763, 911] [16, 36, 88, 420, 524, 708, 912] [17, 37, 89, 421, 525, 709, 912] [18, 38, 90, 422, 526, 710, 912] [19, 39, 91, 423, 527, 711, 912] [12, 32, 352, 416, 516, 532, 913] [13, 33, 353, 417, 517, 533, 913] [14, 34, 354, 418, 518, 534, 913] [15, 35, 355, 419, 519, 535, 913] [8, 28, 268, 384, 412, 688, 914] [9, 29, 269, 385, 413, 689, 914] [10, 30, 270, 386, 414, 690, 914] [11, 31, 271, 387, 415, 691, 914] [24, 236, 244, 396, 408, 688, 915] [25, 237, 245, 397, 409, 689, 915] [26, 238, 246, 398, 410, 690, 915] [27, 239, 247, 399, 411, 691, 915] [20, 36, 44, 404, 580, 668, 916] [21, 37, 45, 405, 581, 669, 916] [22, 38, 46, 406, 582, 670, 916] [23, 39, 47, 407, 583, 671, 916] [4, 16, 236, 400, 664, 676, 917] [5, 17, 237, 401, 665, 677, 917] [6, 18, 238, 402, 666, 678, 917] [7, 19, 239, 403, 667, 679, 917] [12, 220, 228, 396, 412, 472, 918] [13, 221, 229, 397, 413, 473, 918] [14, 222, 230, 398, 414, 474, 918] [15, 223, 231, 399, 415, 475, 918] [8, 96, 212, 392, 504, 644, 919] [9, 97, 213, 393, 505, 645, 919] [10, 98, 214, 394, 506, 646, 919] [11, 99, 215, 395, 507, 647, 919] [0, 4, 288, 388, 616, 632, 920] [1, 5, 289, 389, 617, 633, 920] [2, 6, 290, 390, 618, 634, 920] [3, 7, 291, 391, 619, 635, 920] [20, 40, 184, 424, 520, 712, 921] [21, 41, 185, 425, 521, 713, 921] [22, 42, 186, 426, 522, 714, 921] [23, 43, 187, 427, 523, 715, 921] [40, 88, 332, 456, 472, 584, 922] [41, 89, 333, 457, 473, 585, 922] [42, 90, 334, 458, 474, 586, 922] [43, 91, 335, 459, 475, 587, 922] [48, 92, 340, 396, 476, 600, 923] [49, 93, 341, 397, 477, 601, 923] [50, 94, 342, 398, 478, 602, 923] [51, 95, 343, 399, 479, 603, 923] [52, 96, 272, 460, 480, 744, 924] [53, 97, 273, 461, 481, 745, 924] [54, 98, 274, 462, 482, 746, 924] [55, 99, 275, 463, 483, 747, 924] [128, 180, 240, 548, 564, 744, 925] [129, 181, 241, 549, 565, 745, 925] [130, 182, 242, 550, 566, 746, 925] [131, 183, 243, 551, 567, 747, 925] [112, 176, 372, 408, 488, 560, 926] [113, 177, 373, 409, 489, 561, 926] [114, 178, 374, 410, 490, 562, 926] [115, 179, 375, 411, 491, 563, 926] [172, 224, 232, 404, 556, 700, 927] [173, 225, 233, 405, 557, 701, 927] [174, 226, 234, 406, 558, 702, 927] [175, 227, 235, 407, 559, 703, 927] [116, 168, 372, 400, 552, 752, 928] [117, 169, 373, 401, 553, 753, 928] [118, 170, 374, 402, 554, 754, 928] [119, 171, 375, 403, 555, 755, 928] [112, 164, 224, 480, 548, 672, 929] [113, 165, 225, 481, 549, 673, 929] [114, 166, 226, 482, 550, 674, 929] [115, 167, 227, 483, 551, 675, 929] [100, 160, 312, 528, 544, 620, 930] [101, 161, 313, 529, 545, 621, 930] [102, 162, 314, 530, 546, 622, 930] [103, 163, 315, 531, 547, 623, 930] [156, 216, 308, 524, 540, 624, 931] [157, 217, 309, 525, 541, 625, 931] [158, 218, 310, 526, 542, 626, 931] [159, 219, 311, 527, 543, 627, 931] [140, 200, 292, 492, 524, 656, 932] [141, 201, 293, 493, 525, 657, 932] [142, 202, 294, 494, 526, 658, 932] [143, 203, 295, 495, 527, 659, 932] [136, 196, 356, 496, 520, 652, 933] [137, 197, 357, 497, 521, 653, 933] [138, 198, 358, 498, 522, 654, 933] [139, 199, 359, 499, 523, 655, 933] [88, 132, 180, 500, 516, 720, 934] [89, 133, 181, 501, 517, 721, 934] [90, 134, 182, 502, 518, 722, 934] [91, 135, 183, 503, 519, 723, 934] [16, 84, 128, 496, 512, 724, 935] [17, 85, 129, 497, 513, 725, 935] [18, 86, 130, 498, 514, 726, 935] [19, 87, 131, 499, 515, 727, 935] [0, 1, 2, 3, 768, 839, 842] [4, 5, 6, 7, 776, 780, 836] [8, 9, 10, 11, 773, 835] [12, 13, 14, 15, 830, 834, 838] [16, 17, 18, 19, 778, 792, 833] [20, 21, 22, 23, 790, 791, 832] [24, 25, 26, 27, 810, 831, 834] [28, 29, 30, 31, 768, 810, 830] [32, 33, 34, 35, 829, 849] [36, 37, 38, 39, 805, 828, 851] [40, 41, 42, 43, 804, 837] [44, 45, 46, 47, 827, 829] [48, 49, 50, 51, 783, 825, 846] [52, 53, 54, 55, 801, 824, 837] [56, 57, 58, 59, 800, 823, 828] [60, 61, 62, 63, 813, 822, 825] [64, 65, 66, 67, 787, 816, 821] [68, 69, 70, 71, 815, 820] [72, 73, 74, 75, 768, 784, 819] [76, 77, 78, 79, 798, 814, 818] [80, 81, 82, 83, 817, 821] [84, 85, 86, 87, 795, 820, 826] [88, 89, 90, 91, 788, 819, 838] [92, 93, 94, 95, 784, 834, 839] [96, 97, 98, 99, 796, 818, 840] [100, 101, 102, 103, 795, 832] [104, 105, 106, 107, 838, 839] [108, 109, 110, 111, 779, 823] [112, 113, 114, 115, 777, 824] [116, 117, 118, 119, 799, 836] [120, 121, 122, 123, 793, 825] [124, 125, 126, 127, 800] [128, 129, 130, 131, 801] [132, 133, 134, 135, 803] [136, 137, 138, 139, 771] [140, 141, 142, 143, 770, 851] [144, 145, 146, 147, 793, 835, 850] [148, 149, 150, 151, 836, 849] [152, 153, 154, 155, 777, 848] [156, 157, 158, 159, 779, 847, 851] [160, 161, 162, 163, 789, 846, 850] [164, 165, 166, 167, 802, 840, 845] [168, 169, 170, 171, 794, 833, 844] [172, 173, 174, 175, 807, 832, 843] [176, 177, 178, 179, 831, 842] [180, 181, 182, 183, 796, 841, 845] [184, 185, 186, 187, 797, 816, 844] [188, 189, 190, 191, 811, 815, 843] [192, 193, 194, 195, 808, 814, 845] [196, 197, 198, 199, 790, 807, 820] [200, 201, 202, 203, 788, 830, 842] [204, 205, 206, 207, 787, 833] [208, 209, 210, 211, 786, 802, 814] [212, 213, 214, 215, 785, 790, 815] [216, 217, 218, 219, 784, 788, 831] [220, 221, 222, 223, 783, 813, 835] [224, 225, 226, 227, 770, 782, 828] [228, 229, 230, 231, 771, 781, 837] [232, 233, 234, 235, 772, 780, 827] [236, 237, 238, 239, 773, 783, 789] [240, 241, 242, 243, 774, 779, 782] [244, 245, 246, 247, 775, 777, 781] [248, 249, 250, 251, 776, 799, 829] [252, 253, 254, 255, 775, 804, 824] [256, 257, 258, 259, 774, 805, 823] [260, 261, 262, 263, 773, 806, 822] [264, 265, 266, 267, 772, 776] [268, 269, 270, 271, 771, 775] [272, 273, 274, 275, 770, 774] [276, 277, 278, 279, 769, 808, 818] [280, 281, 282, 283, 778, 809, 817] [284, 285, 286, 287, 785, 791, 826] [288, 289, 290, 291, 769, 802, 812] [292, 293, 294, 295, 792, 794, 821] [296, 297, 298, 299, 798, 812, 840] [300, 301, 302, 303, 791, 811] [304, 305, 306, 307, 810, 819] [308, 309, 310, 311, 792, 809, 816] [312, 313, 314, 315, 808, 812, 841] [316, 317, 318, 319, 807, 811, 826] [320, 321, 322, 323, 806, 846] [324, 325, 326, 327, 805, 847] [328, 329, 330, 331, 804, 848] [332, 333, 334, 335, 806, 813, 850] [336, 337, 338, 339, 780, 803, 849] [340, 341, 342, 343, 781, 801, 848] [344, 345, 346, 347, 782, 800, 847] [348, 349, 350, 351, 799, 803, 827] [352, 353, 354, 355, 786, 798, 841] [356, 357, 358, 359, 778, 787, 797] [360, 361, 362, 363, 769, 786, 796] [364, 365, 366, 367, 785, 795, 843] [368, 369, 370, 371, 794, 797, 817] [372, 373, 374, 375, 789, 793, 822] [376, 377, 378, 379, 772] [380, 381, 382, 383, 809, 844] [384, 385, 386, 387, 768] [388, 389, 390, 391, 768, 802, 836] [392, 393, 394, 395, 785, 835, 840] [396, 397, 398, 399, 781, 783, 834] [400, 401, 402, 403, 789, 833, 836] [404, 405, 406, 407, 827, 828, 832] [408, 409, 410, 411, 777, 789, 831] [412, 413, 414, 415, 771, 830, 835] [416, 417, 418, 419, 798, 829, 834] [420, 421, 422, 423, 828, 833, 838] [424, 425, 426, 427, 816, 832, 837] [428, 429, 430, 431, 818, 827, 831] [432, 433, 434, 435, 811, 814, 825] [436, 437, 438, 439, 809, 824] [440, 441, 442, 443, 787, 823] [444, 445, 446, 447, 786, 807, 822] [448, 449, 450, 451, 806, 821, 829] [452, 453, 454, 455, 820] [456, 457, 458, 459, 804, 806, 819] [460, 461, 462, 463, 818, 837] [464, 465, 466, 467, 813, 817, 827] [468, 469, 470, 471, 826] [472, 473, 474, 475, 813, 837, 838] [476, 477, 478, 479, 801, 825, 839] [480, 481, 482, 483, 770, 824, 840] [484, 485, 486, 487, 799, 823] [488, 489, 490, 491, 822, 824] [492, 493, 494, 495, 821, 842] [496, 497, 498, 499, 778, 820] [500, 501, 502, 503, 819, 845] [504, 505, 506, 507, 815, 818] [508, 509, 510, 511, 768, 817] [512, 513, 514, 515, 826, 833] [516, 517, 518, 519, 838, 841] [520, 521, 522, 523, 790, 797] [524, 525, 526, 527, 788, 792, 851] [528, 529, 530, 531, 795, 812, 850] [532, 533, 534, 535, 786, 830, 849] [536, 537, 538, 539, 785, 794, 848] [540, 541, 542, 543, 784, 809, 847] [544, 545, 546, 547, 808, 846] [548, 549, 550, 551, 782, 845] [552, 553, 554, 555, 793, 844] [556, 557, 558, 559, 780, 782, 843] [560, 561, 562, 563, 793, 842] [564, 565, 566, 567, 779, 841] [568, 569, 570, 571, 816] [572, 573, 574, 575, 779, 815, 836] [576, 577, 578, 579, 800, 814] [580, 581, 582, 583, 790, 851] [584, 585, 586, 587, 788, 850] [588, 589, 590, 591, 787, 846, 849] [592, 593, 594, 595, 786, 823, 848] [596, 597, 598, 599, 785, 847, 849] [600, 601, 602, 603, 784, 846, 848] [604, 605, 606, 607, 783, 791, 845] [608, 609, 610, 611, 782, 834, 844] [612, 613, 614, 615, 781, 821, 843] [616, 617, 618, 619, 769, 780, 842] [620, 621, 622, 623, 789, 832, 841] [624, 625, 626, 627, 779, 816, 831] [628, 629, 630, 631, 777, 815, 817] [632, 633, 634, 635, 776, 812, 839] [636, 637, 638, 639, 775, 811] [640, 641, 642, 643, 774, 797, 810] [644, 645, 646, 647, 773, 790, 796] [648, 649, 650, 651, 772, 808] [652, 653, 654, 655, 771, 787, 807] [656, 657, 658, 659, 770, 794, 830] [660, 661, 662, 663, 769, 781, 805] [664, 665, 666, 667, 778, 780, 783] [668, 669, 670, 671, 791, 805, 829] [672, 673, 674, 675, 777, 802, 828] [676, 677, 678, 679, 773, 776, 792] [680, 681, 682, 683, 775, 812, 851] [684, 685, 686, 687, 774, 776, 811] [688, 689, 690, 691, 773, 775, 810] [692, 693, 694, 695, 772, 809, 835] [696, 697, 698, 699, 771, 808, 847] [700, 701, 702, 703, 770, 772, 807] [704, 705, 706, 707, 769, 806, 820] [708, 709, 710, 711, 778, 805, 819] [712, 713, 714, 715, 791, 804, 844] [716, 717, 718, 719, 802, 813, 826] [720, 721, 722, 723, 788, 796, 803] [724, 725, 726, 727, 792, 795, 801] [728, 729, 730, 731, 800, 839] [732, 733, 734, 735, 784, 799, 840] [736, 737, 738, 739, 798, 804] [740, 741, 742, 743, 797, 803, 825] [744, 745, 746, 747, 774, 796, 801] [748, 749, 750, 751, 795, 800, 803] [752, 753, 754, 755, 794, 799, 822] [756, 757, 758, 759, 793, 798, 843] [760, 761, 762, 763, 810, 814] [764, 765, 766, 767, 850]
H_Z (528 checks, sparse supports)
[0, 28, 72, 384, 388, 508, 768] [1, 29, 73, 385, 389, 509, 768] [2, 30, 74, 386, 390, 510, 768] [3, 31, 75, 387, 391, 511, 768] [276, 288, 360, 616, 660, 704, 769] [277, 289, 361, 617, 661, 705, 769] [278, 290, 362, 618, 662, 706, 769] [279, 291, 363, 619, 663, 707, 769] [140, 224, 272, 480, 656, 700, 770] [141, 225, 273, 481, 657, 701, 770] [142, 226, 274, 482, 658, 702, 770] [143, 227, 275, 483, 659, 703, 770] [136, 228, 268, 412, 652, 696, 771] [137, 229, 269, 413, 653, 697, 771] [138, 230, 270, 414, 654, 698, 771] [139, 231, 271, 415, 655, 699, 771] [232, 264, 376, 648, 692, 700, 772] [233, 265, 377, 649, 693, 701, 772] [234, 266, 378, 650, 694, 702, 772] [235, 267, 379, 651, 695, 703, 772] [8, 236, 260, 644, 676, 688, 773] [9, 237, 261, 645, 677, 689, 773] [10, 238, 262, 646, 678, 690, 773] [11, 239, 263, 647, 679, 691, 773] [240, 256, 272, 640, 684, 744, 774] [241, 257, 273, 641, 685, 745, 774] [242, 258, 274, 642, 686, 746, 774] [243, 259, 275, 643, 687, 747, 774] [244, 252, 268, 636, 680, 688, 775] [245, 253, 269, 637, 681, 689, 775] [246, 254, 270, 638, 682, 690, 775] [247, 255, 271, 639, 683, 691, 775] [4, 248, 264, 632, 676, 684, 776] [5, 249, 265, 633, 677, 685, 776] [6, 250, 266, 634, 678, 686, 776] [7, 251, 267, 635, 679, 687, 776] [112, 152, 244, 408, 628, 672, 777] [113, 153, 245, 409, 629, 673, 777] [114, 154, 246, 410, 630, 674, 777] [115, 155, 247, 411, 631, 675, 777] [16, 280, 356, 496, 664, 708, 778] [17, 281, 357, 497, 665, 709, 778] [18, 282, 358, 498, 666, 710, 778] [19, 283, 359, 499, 667, 711, 778] [108, 156, 240, 564, 572, 624, 779] [109, 157, 241, 565, 573, 625, 779] [110, 158, 242, 566, 574, 626, 779] [111, 159, 243, 567, 575, 627, 779] [4, 232, 336, 556, 616, 664, 780] [5, 233, 337, 557, 617, 665, 780] [6, 234, 338, 558, 618, 666, 780] [7, 235, 339, 559, 619, 667, 780] [228, 244, 340, 396, 612, 660, 781] [229, 245, 341, 397, 613, 661, 781] [230, 246, 342, 398, 614, 662, 781] [231, 247, 343, 399, 615, 663, 781] [224, 240, 344, 548, 556, 608, 782] [225, 241, 345, 549, 557, 609, 782] [226, 242, 346, 550, 558, 610, 782] [227, 243, 347, 551, 559, 611, 782] [48, 220, 236, 396, 604, 664, 783] [49, 221, 237, 397, 605, 665, 783] [50, 222, 238, 398, 606, 666, 783] [51, 223, 239, 399, 607, 667, 783] [72, 92, 216, 540, 600, 732, 784] [73, 93, 217, 541, 601, 733, 784] [74, 94, 218, 542, 602, 734, 784] [75, 95, 219, 543, 603, 735, 784] [212, 284, 364, 392, 536, 596, 785] [213, 285, 365, 393, 537, 597, 785] [214, 286, 366, 394, 538, 598, 785] [215, 287, 367, 395, 539, 599, 785] [208, 352, 360, 444, 532, 592, 786] [209, 353, 361, 445, 533, 593, 786] [210, 354, 362, 446, 534, 594, 786] [211, 355, 363, 447, 535, 595, 786] [64, 204, 356, 440, 588, 652, 787] [65, 205, 357, 441, 589, 653, 787] [66, 206, 358, 442, 590, 654, 787] [67, 207, 359, 443, 591, 655, 787] [88, 200, 216, 524, 584, 720, 788] [89, 201, 217, 525, 585, 721, 788] [90, 202, 218, 526, 586, 722, 788] [91, 203, 219, 527, 587, 723, 788] [160, 236, 372, 400, 408, 620, 789] [161, 237, 373, 401, 409, 621, 789] [162, 238, 374, 402, 410, 622, 789] [163, 239, 375, 403, 411, 623, 789] [20, 196, 212, 520, 580, 644, 790] [21, 197, 213, 521, 581, 645, 790] [22, 198, 214, 522, 582, 646, 790] [23, 199, 215, 523, 583, 647, 790] [20, 284, 300, 604, 668, 712, 791] [21, 285, 301, 605, 669, 713, 791] [22, 286, 302, 606, 670, 714, 791] [23, 287, 303, 607, 671, 715, 791] [16, 292, 308, 524, 676, 724, 792] [17, 293, 309, 525, 677, 725, 792] [18, 294, 310, 526, 678, 726, 792] [19, 295, 311, 527, 679, 727, 792] [120, 144, 372, 552, 560, 756, 793] [121, 145, 373, 553, 561, 757, 793] [122, 146, 374, 554, 562, 758, 793] [123, 147, 375, 555, 563, 759, 793] [168, 292, 368, 536, 656, 752, 794] [169, 293, 369, 537, 657, 753, 794] [170, 294, 370, 538, 658, 754, 794] [171, 295, 371, 539, 659, 755, 794] [84, 100, 364, 528, 724, 748, 795] [85, 101, 365, 529, 725, 749, 795] [86, 102, 366, 530, 726, 750, 795] [87, 103, 367, 531, 727, 751, 795] [96, 180, 360, 644, 720, 744, 796] [97, 181, 361, 645, 721, 745, 796] [98, 182, 362, 646, 722, 746, 796] [99, 183, 363, 647, 723, 747, 796] [184, 356, 368, 520, 640, 740, 797] [185, 357, 369, 521, 641, 741, 797] [186, 358, 370, 522, 642, 742, 797] [187, 359, 371, 523, 643, 743, 797] [76, 296, 352, 416, 736, 756, 798] [77, 297, 353, 417, 737, 757, 798] [78, 298, 354, 418, 738, 758, 798] [79, 299, 355, 419, 739, 759, 798] [116, 248, 348, 484, 732, 752, 799] [117, 249, 349, 485, 733, 753, 799] [118, 250, 350, 486, 734, 754, 799] [119, 251, 351, 487, 735, 755, 799] [56, 124, 344, 576, 728, 748, 800] [57, 125, 345, 577, 729, 749, 800] [58, 126, 346, 578, 730, 750, 800] [59, 127, 347, 579, 731, 751, 800] [52, 128, 340, 476, 724, 744, 801] [53, 129, 341, 477, 725, 745, 801] [54, 130, 342, 478, 726, 746, 801] [55, 131, 343, 479, 727, 747, 801] [164, 208, 288, 388, 672, 716, 802] [165, 209, 289, 389, 673, 717, 802] [166, 210, 290, 390, 674, 718, 802] [167, 211, 291, 391, 675, 719, 802] [132, 336, 348, 720, 740, 748, 803] [133, 337, 349, 721, 741, 749, 803] [134, 338, 350, 722, 742, 750, 803] [135, 339, 351, 723, 743, 751, 803] [40, 252, 328, 456, 712, 736, 804] [41, 253, 329, 457, 713, 737, 804] [42, 254, 330, 458, 714, 738, 804] [43, 255, 331, 459, 715, 739, 804] [36, 256, 324, 660, 668, 708, 805] [37, 257, 325, 661, 669, 709, 805] [38, 258, 326, 662, 670, 710, 805] [39, 259, 327, 663, 671, 711, 805] [260, 320, 332, 448, 456, 704, 806] [261, 321, 333, 449, 457, 705, 806] [262, 322, 334, 450, 458, 706, 806] [263, 323, 335, 451, 459, 707, 806] [172, 196, 316, 444, 652, 700, 807] [173, 197, 317, 445, 653, 701, 807] [174, 198, 318, 446, 654, 702, 807] [175, 199, 319, 447, 655, 703, 807] [192, 276, 312, 544, 648, 696, 808] [193, 277, 313, 545, 649, 697, 808] [194, 278, 314, 546, 650, 698, 808] [195, 279, 315, 547, 651, 699, 808] [280, 308, 380, 436, 540, 692, 809] [281, 309, 381, 437, 541, 693, 809] [282, 310, 382, 438, 542, 694, 809] [283, 311, 383, 439, 543, 695, 809] [24, 28, 304, 640, 688, 760, 810] [25, 29, 305, 641, 689, 761, 810] [26, 30, 306, 642, 690, 762, 810] [27, 31, 307, 643, 691, 763, 810] [188, 300, 316, 432, 636, 684, 811] [189, 301, 317, 433, 637, 685, 811] [190, 302, 318, 434, 638, 686, 811] [191, 303, 319, 435, 639, 687, 811] [288, 296, 312, 528, 632, 680, 812] [289, 297, 313, 529, 633, 681, 812] [290, 298, 314, 530, 634, 682, 812] [291, 299, 315, 531, 635, 683, 812] [60, 220, 332, 464, 472, 716, 813] [61, 221, 333, 465, 473, 717, 813] [62, 222, 334, 466, 474, 718, 813] [63, 223, 335, 467, 475, 719, 813] [76, 192, 208, 432, 576, 760, 814] [77, 193, 209, 433, 577, 761, 814] [78, 194, 210, 434, 578, 762, 814] [79, 195, 211, 435, 579, 763, 814] [68, 188, 212, 504, 572, 628, 815] [69, 189, 213, 505, 573, 629, 815] [70, 190, 214, 506, 574, 630, 815] [71, 191, 215, 507, 575, 631, 815] [64, 184, 308, 424, 568, 624, 816] [65, 185, 309, 425, 569, 625, 816] [66, 186, 310, 426, 570, 626, 816] [67, 187, 311, 427, 571, 627, 816] [80, 280, 368, 464, 508, 628, 817] [81, 281, 369, 465, 509, 629, 817] [82, 282, 370, 466, 510, 630, 817] [83, 283, 371, 467, 511, 631, 817] [76, 96, 276, 428, 460, 504, 818] [77, 97, 277, 429, 461, 505, 818] [78, 98, 278, 430, 462, 506, 818] [79, 99, 279, 431, 463, 507, 818] [72, 88, 304, 456, 500, 708, 819] [73, 89, 305, 457, 501, 709, 819] [74, 90, 306, 458, 502, 710, 819] [75, 91, 307, 459, 503, 711, 819] [68, 84, 196, 452, 496, 704, 820] [69, 85, 197, 453, 497, 705, 820] [70, 86, 198, 454, 498, 706, 820] [71, 87, 199, 455, 499, 707, 820] [64, 80, 292, 448, 492, 612, 821] [65, 81, 293, 449, 493, 613, 821] [66, 82, 294, 450, 494, 614, 821] [67, 83, 295, 451, 495, 615, 821] [60, 260, 372, 444, 488, 752, 822] [61, 261, 373, 445, 489, 753, 822] [62, 262, 374, 446, 490, 754, 822] [63, 263, 375, 447, 491, 755, 822] [56, 108, 256, 440, 484, 592, 823] [57, 109, 257, 441, 485, 593, 823] [58, 110, 258, 442, 486, 594, 823] [59, 111, 259, 443, 487, 595, 823] [52, 112, 252, 436, 480, 488, 824] [53, 113, 253, 437, 481, 489, 824] [54, 114, 254, 438, 482, 490, 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Code ID 936-48-12 · download JSON · raw on GitHub