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[[948,24,28]] d ≤
n
948
k
24
d
28
kd²/n
19.848
w
7
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 28, d_Z ≤ 28 · 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 28 · witness weight 28 (claimed upper_bound)
witness operator (support, 28 qubits)
[40, 41, 200, 201, 380, 381, 420, 421, 460, 461, 496, 497, 536, 537, 572, 573, 592, 593, 628, 629, 640, 641, 648, 649, 692, 693, 764, 765]
d_Z 28 · witness weight 28 (claimed upper_bound)
witness operator (support, 28 qubits)
[24, 25, 28, 29, 80, 81, 124, 125, 156, 157, 284, 285, 416, 417, 436, 437, 544, 545, 564, 565, 608, 609, 652, 653, 696, 697, 756, 757]
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 6.935) · H_Z 5–7 (mean 6.935)
qubit degrees H_X 2–6 (mean 4.038) · H_Z 2–6 (mean 4.038)
trapping sets H_X (1,2)×12 (2,2)×18 (3,2)×18 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,2): 12 (1,3): 120 (1,4): 726 (1,6): 90 (2,2): 18 (2,3): 8 (2,4): 320 (2,5): 1280 (2,6): 7114 (2,7): 312 (2,8): 1820 (2,10): 508 (3,2): 18 (3,3): 24 (3,4): 552 (3,5): 572 (3,6): 8574 (3,7): 22060 (3,8): 98858 (3,9): 11536 (3,10): 48952 (3,11): 2888 (3,12): 19922 (3,13): 272 (3,14): 6513 (3,16): 160
trapping sets H_Z (1,2)×16 (2,2)×24 (3,2)×24 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,2): 16 (1,3): 112 (1,4): 730 (1,6): 90 (2,2): 24 (2,4): 316 (2,5): 1240 (2,6): 7172 (2,7): 288 (2,8): 1832 (2,10): 507 (3,2): 24 (3,4): 592 (3,5): 440 (3,6): 8576 (3,7): 21640 (3,8): 99496 (3,9): 11256 (3,10): 49364 (3,11): 2648 (3,12): 20036 (3,13): 248 (3,14): 6511 (3,16): 159

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 [[192,12,14]] entry, using a sparse independent-row presentation of its checks: n' = 4n + m_X + m_Z = 948, k' = 2k = 24, 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 28/28); 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

[[948,24,28]] — one [[4,2,2]] distance-amplification step of [[192,12,14]]

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 28 / 28 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/192-12-14.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 552 (max weight 7) · Z-checks 552 (max weight 7)
H_X (552 checks, sparse supports)
[0, 40, 260, 384, 536, 672, 858] [1, 41, 261, 385, 537, 673, 858] [2, 42, 262, 386, 538, 674, 858] [3, 43, 263, 387, 539, 675, 858] [148, 224, 276, 452, 660, 728, 859] [149, 225, 277, 453, 661, 729, 859] [150, 226, 278, 454, 662, 730, 859] [151, 227, 279, 455, 663, 731, 859] [84, 216, 272, 536, 548, 656, 860] [85, 217, 273, 537, 549, 657, 860] [86, 218, 274, 538, 550, 658, 860] [87, 219, 275, 539, 551, 659, 860] [80, 268, 368, 396, 444, 652, 861] [81, 269, 369, 397, 445, 653, 861] [82, 270, 370, 398, 446, 654, 861] [83, 271, 371, 399, 447, 655, 861] [76, 208, 264, 440, 648, 668, 862] [77, 209, 265, 441, 649, 669, 862] [78, 210, 266, 442, 650, 670, 862] [79, 211, 267, 443, 651, 671, 862] [72, 260, 364, 400, 644, 720, 863] [73, 261, 365, 401, 645, 721, 863] [74, 262, 366, 402, 646, 722, 863] [75, 263, 367, 403, 647, 723, 863] [68, 200, 256, 520, 640, 672, 864] [69, 201, 257, 521, 641, 673, 864] [70, 202, 258, 522, 642, 674, 864] [71, 203, 259, 523, 643, 675, 864] [64, 252, 356, 432, 472, 636, 865] [65, 253, 357, 433, 473, 637, 865] [66, 254, 358, 434, 474, 638, 865] [67, 255, 359, 435, 475, 639, 865] [192, 248, 352, 468, 632, 728, 866] [193, 249, 353, 469, 633, 729, 866] [194, 250, 354, 470, 634, 730, 866] [195, 251, 355, 471, 635, 731, 866] [188, 244, 292, 508, 588, 628, 867] [189, 245, 293, 509, 589, 629, 867] [190, 246, 294, 510, 590, 630, 867] [191, 247, 295, 511, 591, 631, 867] [152, 280, 372, 432, 456, 664, 868] [153, 281, 373, 433, 457, 665, 868] [154, 282, 374, 434, 458, 666, 868] [155, 283, 375, 435, 459, 667, 868] [184, 196, 240, 412, 428, 624, 869] [185, 197, 241, 413, 429, 625, 869] [186, 198, 242, 414, 430, 626, 869] [187, 199, 243, 415, 431, 627, 869] [96, 176, 232, 576, 616, 704, 870] [97, 177, 233, 577, 617, 705, 870] [98, 178, 234, 578, 618, 706, 870] [99, 179, 235, 579, 619, 707, 870] [172, 228, 368, 492, 612, 764, 871] [173, 229, 369, 493, 613, 765, 871] [174, 230, 370, 494, 614, 766, 871] [175, 231, 371, 495, 615, 767, 871] [168, 224, 316, 416, 608, 688, 872] [169, 225, 317, 417, 609, 689, 872] [170, 226, 318, 418, 610, 690, 872] [171, 227, 319, 419, 611, 691, 872] [104, 164, 220, 604, 684, 712, 873] [105, 165, 221, 605, 685, 713, 873] [106, 166, 222, 606, 686, 714, 873] [107, 167, 223, 607, 687, 715, 873] [120, 160, 216, 492, 600, 692, 874] [121, 161, 217, 493, 601, 693, 874] [122, 162, 218, 494, 602, 694, 874] [123, 163, 219, 495, 603, 695, 874] [156, 212, 240, 480, 596, 756, 875] [157, 213, 241, 481, 597, 757, 875] [158, 214, 242, 482, 598, 758, 875] [159, 215, 243, 483, 599, 759, 875] [132, 152, 208, 412, 592, 616, 876] [133, 153, 209, 413, 593, 617, 876] [134, 154, 210, 414, 594, 618, 876] [135, 155, 211, 415, 595, 619, 876] [128, 148, 204, 588, 612, 700, 877] [129, 149, 205, 589, 613, 701, 877] [130, 150, 206, 590, 614, 702, 877] [131, 151, 207, 591, 615, 703, 877] [144, 200, 372, 584, 624, 676, 878] [145, 201, 373, 585, 625, 677, 878] [146, 202, 374, 586, 626, 678, 878] [147, 203, 375, 587, 627, 679, 878] [180, 236, 304, 424, 620, 700, 879] [181, 237, 305, 425, 621, 701, 879] [182, 238, 306, 426, 622, 702, 879] [183, 239, 307, 427, 623, 703, 879] [140, 196, 224, 580, 620, 744, 880] [141, 197, 225, 581, 621, 745, 880] [142, 198, 226, 582, 622, 746, 880] [143, 199, 227, 583, 623, 747, 880] [156, 232, 284, 552, 632, 668, 881] [157, 233, 285, 553, 633, 669, 881] [158, 234, 286, 554, 634, 670, 881] [159, 235, 287, 555, 635, 671, 881] [228, 248, 292, 512, 676, 748, 882] [229, 249, 293, 513, 677, 749, 882] [230, 250, 294, 514, 678, 750, 882] [231, 251, 295, 515, 679, 751, 882] [28, 352, 372, 580, 612, 756, 883] [29, 353, 373, 581, 613, 757, 883] [30, 354, 374, 582, 614, 758, 883] [31, 355, 375, 583, 615, 759, 883] [40, 348, 368, 496, 596, 752, 884] [41, 349, 369, 497, 597, 753, 884] [42, 350, 370, 498, 598, 754, 884] [43, 351, 371, 499, 599, 755, 884] [108, 344, 364, 504, 680, 748, 885] [109, 345, 365, 505, 681, 749, 885] [110, 346, 366, 506, 682, 750, 885] [111, 347, 367, 507, 683, 751, 885] [32, 340, 360, 388, 584, 744, 886] [33, 341, 361, 389, 585, 745, 886] [34, 342, 362, 390, 586, 746, 886] [35, 343, 363, 391, 587, 747, 886] [328, 336, 356, 580, 628, 740, 887] [329, 337, 357, 581, 629, 741, 887] [330, 338, 358, 582, 630, 742, 887] [331, 339, 359, 583, 631, 743, 887] [264, 324, 352, 524, 556, 736, 888] [265, 325, 353, 525, 557, 737, 888] [266, 326, 354, 526, 558, 738, 888] [267, 327, 355, 527, 559, 739, 888] [180, 312, 348, 452, 540, 732, 889] [181, 313, 349, 453, 541, 733, 889] [182, 314, 350, 454, 542, 734, 889] [183, 315, 351, 455, 543, 735, 889] [172, 304, 344, 460, 636, 728, 890] [173, 305, 345, 461, 637, 729, 890] [174, 306, 346, 462, 638, 730, 890] [175, 307, 347, 463, 639, 731, 890] [168, 340, 380, 384, 528, 724, 891] [169, 341, 381, 385, 529, 725, 891] [170, 342, 382, 386, 530, 726, 891] [171, 343, 383, 387, 531, 727, 891] [240, 288, 336, 440, 468, 672, 892] [241, 289, 337, 441, 469, 673, 892] [242, 290, 338, 442, 470, 674, 892] [243, 291, 339, 443, 471, 675, 892] [164, 296, 336, 524, 572, 720, 893] [165, 297, 337, 525, 573, 721, 893] [166, 298, 338, 526, 574, 722, 893] [167, 299, 339, 527, 575, 723, 893] [204, 284, 328, 608, 676, 712, 894] [205, 285, 329, 609, 677, 713, 894] [206, 286, 330, 610, 678, 714, 894] [207, 287, 331, 611, 679, 715, 894] [100, 280, 324, 476, 500, 708, 895] [101, 281, 325, 477, 501, 709, 895] [102, 282, 326, 478, 502, 710, 895] [103, 283, 327, 479, 503, 711, 895] [216, 276, 320, 496, 704, 748, 896] [217, 277, 321, 497, 705, 749, 896] [218, 278, 322, 498, 706, 750, 896] [219, 279, 323, 499, 707, 751, 896] [36, 272, 316, 592, 604, 700, 897] [37, 273, 317, 593, 605, 701, 897] [38, 274, 318, 594, 606, 702, 897] [39, 275, 319, 595, 607, 703, 897] [4, 268, 312, 416, 488, 696, 898] [5, 269, 313, 417, 489, 697, 898] [6, 270, 314, 418, 490, 698, 898] [7, 271, 315, 419, 491, 699, 898] [244, 264, 308, 484, 692, 712, 899] [245, 265, 309, 485, 693, 713, 899] [246, 266, 310, 486, 694, 714, 899] [247, 267, 311, 487, 695, 715, 899] [220, 260, 304, 420, 688, 740, 900] [221, 261, 305, 421, 689, 741, 900] [222, 262, 306, 422, 690, 742, 900] [223, 263, 307, 423, 691, 743, 900] [256, 300, 324, 576, 684, 716, 901] [257, 301, 325, 577, 685, 717, 901] [258, 302, 326, 578, 686, 718, 901] [259, 303, 327, 579, 687, 719, 901] [232, 252, 296, 476, 516, 680, 902] [233, 253, 297, 477, 517, 681, 902] [234, 254, 298, 478, 518, 682, 902] [235, 255, 299, 479, 519, 683, 902] [92, 288, 332, 484, 512, 716, 903] [93, 289, 333, 485, 513, 717, 903] [94, 290, 334, 486, 514, 718, 903] [95, 291, 335, 487, 515, 719, 903] [116, 136, 192, 428, 576, 688, 904] [117, 137, 193, 429, 577, 689, 904] [118, 138, 194, 430, 578, 690, 904] [119, 139, 195, 431, 579, 691, 904] [132, 188, 256, 464, 532, 572, 905] [133, 189, 257, 465, 533, 573, 905] [134, 190, 258, 466, 534, 574, 905] [135, 191, 259, 467, 535, 575, 905] [184, 252, 332, 392, 408, 568, 906] [185, 253, 333, 393, 409, 569, 906] [186, 254, 334, 394, 410, 570, 906] [187, 255, 335, 395, 411, 571, 906] [80, 136, 236, 384, 464, 544, 907] [81, 137, 237, 385, 465, 545, 907] [82, 138, 238, 386, 466, 546, 907] [83, 139, 239, 387, 467, 547, 907] [36, 76, 376, 460, 540, 572, 908] [37, 77, 377, 461, 541, 573, 908] [38, 78, 378, 462, 542, 574, 908] [39, 79, 379, 463, 543, 575, 908] [8, 72, 228, 456, 548, 724, 909] [9, 73, 229, 457, 549, 725, 909] [10, 74, 230, 458, 550, 726, 909] [11, 75, 231, 459, 551, 727, 909] [32, 68, 272, 452, 664, 720, 910] [33, 69, 273, 453, 665, 721, 910] [34, 70, 274, 454, 666, 722, 910] [35, 71, 275, 455, 667, 723, 910] [64, 220, 268, 448, 528, 560, 911] [65, 221, 269, 449, 529, 561, 911] [66, 222, 270, 450, 530, 562, 911] [67, 223, 271, 451, 531, 563, 911] [0, 60, 212, 444, 532, 664, 912] [1, 61, 213, 445, 533, 665, 912] [2, 62, 214, 446, 534, 666, 912] [3, 63, 215, 447, 535, 667, 912] [28, 56, 188, 440, 652, 660, 913] [29, 57, 189, 441, 653, 661, 913] [30, 58, 190, 442, 654, 662, 913] [31, 59, 191, 443, 655, 663, 913] [52, 184, 204, 436, 456, 544, 914] [53, 185, 205, 437, 457, 545, 914] [54, 186, 206, 438, 458, 546, 914] [55, 187, 207, 439, 459, 547, 914] [48, 176, 196, 432, 464, 760, 915] [49, 177, 197, 433, 465, 761, 915] [50, 178, 198, 434, 466, 762, 915] [51, 179, 199, 435, 467, 763, 915] [44, 84, 140, 400, 468, 732, 916] [45, 85, 141, 401, 469, 733, 916] [46, 86, 142, 402, 470, 734, 916] [47, 87, 143, 403, 471, 735, 916] [24, 44, 360, 428, 504, 696, 917] [25, 45, 361, 429, 505, 697, 917] [26, 46, 362, 430, 506, 698, 917] [27, 47, 363, 431, 507, 699, 917] [16, 36, 300, 420, 488, 516, 918] [17, 37, 301, 421, 489, 517, 918] [18, 38, 302, 422, 490, 518, 918] [19, 39, 303, 423, 491, 519, 918] [12, 32, 208, 416, 680, 756, 919] [13, 33, 209, 417, 681, 757, 919] [14, 34, 210, 418, 682, 758, 919] [15, 35, 211, 419, 683, 759, 919] [8, 28, 236, 412, 608, 752, 920] [9, 29, 237, 413, 609, 753, 920] [10, 30, 238, 414, 610, 754, 920] [11, 31, 239, 415, 611, 755, 920] [24, 48, 128, 408, 460, 652, 921] [25, 49, 129, 409, 461, 653, 921] [26, 50, 130, 410, 462, 654, 921] [27, 51, 131, 411, 463, 655, 921] [4, 20, 344, 404, 568, 648, 922] [5, 21, 345, 405, 569, 649, 922] [6, 22, 346, 406, 570, 650, 922] [7, 23, 347, 407, 571, 651, 922] [16, 120, 340, 400, 444, 472, 923] [17, 121, 341, 401, 445, 473, 923] [18, 122, 342, 402, 446, 474, 923] [19, 123, 343, 403, 447, 475, 923] [12, 112, 160, 396, 636, 736, 924] [13, 113, 161, 397, 637, 737, 924] [14, 114, 162, 398, 638, 738, 924] [15, 115, 163, 399, 639, 739, 924] [8, 88, 100, 392, 552, 732, 925] [9, 89, 101, 393, 553, 733, 925] [10, 90, 102, 394, 554, 734, 925] [11, 91, 103, 395, 555, 735, 925] [0, 4, 296, 388, 592, 716, 926] [1, 5, 297, 389, 593, 717, 926] [2, 6, 298, 390, 594, 718, 926] [3, 7, 299, 391, 595, 719, 926] [20, 40, 356, 424, 624, 692, 927] [21, 41, 357, 425, 625, 693, 927] [22, 42, 358, 426, 626, 694, 927] [23, 43, 359, 427, 627, 695, 927] [88, 144, 244, 436, 472, 564, 928] [89, 145, 245, 437, 473, 565, 928] [90, 146, 246, 438, 474, 566, 928] [91, 147, 247, 439, 475, 567, 928] [48, 92, 320, 476, 508, 764, 929] [49, 93, 321, 477, 509, 765, 929] [50, 94, 322, 478, 510, 766, 929] [51, 95, 323, 479, 511, 767, 929] [44, 52, 96, 480, 500, 600, 930] [45, 53, 97, 481, 501, 601, 930] [46, 54, 98, 482, 502, 602, 930] [47, 55, 99, 483, 503, 603, 930] [124, 180, 248, 404, 564, 656, 931] [125, 181, 249, 405, 565, 657, 931] [126, 182, 250, 406, 566, 658, 931] [127, 183, 251, 407, 567, 659, 931] [60, 176, 328, 520, 560, 660, 932] [61, 177, 329, 521, 561, 661, 932] [62, 178, 330, 522, 562, 662, 932] [63, 179, 331, 523, 563, 663, 932] [56, 116, 172, 448, 556, 760, 933] [57, 117, 173, 449, 557, 761, 933] [58, 118, 174, 450, 558, 762, 933] [59, 119, 175, 451, 559, 763, 933] [52, 168, 320, 396, 552, 644, 934] [53, 169, 321, 397, 553, 645, 934] [54, 170, 322, 398, 554, 646, 934] [55, 171, 323, 399, 555, 647, 934] [108, 164, 348, 548, 640, 668, 935] [109, 165, 349, 549, 641, 669, 935] [110, 166, 350, 550, 642, 670, 935] [111, 167, 351, 551, 643, 671, 935] [24, 160, 316, 448, 544, 648, 936] [25, 161, 317, 449, 545, 649, 936] [26, 162, 318, 450, 546, 650, 936] [27, 163, 319, 451, 547, 651, 936] [20, 104, 156, 436, 540, 736, 937] [21, 105, 157, 437, 541, 737, 937] [22, 106, 158, 438, 542, 738, 937] [23, 107, 159, 439, 543, 739, 937] [16, 152, 308, 392, 536, 560, 938] [17, 153, 309, 393, 537, 561, 938] [18, 154, 310, 394, 538, 562, 938] [19, 155, 311, 395, 539, 563, 938] [96, 148, 288, 532, 556, 656, 939] [97, 149, 289, 533, 557, 657, 939] [98, 150, 290, 534, 558, 658, 939] [99, 151, 291, 535, 559, 659, 939] [12, 144, 300, 528, 568, 632, 940] [13, 145, 301, 529, 569, 633, 940] [14, 146, 302, 530, 570, 634, 940] [15, 147, 303, 531, 571, 635, 940] [92, 140, 284, 524, 564, 724, 941] [93, 141, 285, 525, 565, 725, 941] [94, 142, 286, 526, 566, 726, 941] [95, 143, 287, 527, 567, 727, 941] [136, 280, 292, 408, 520, 644, 942] [137, 281, 293, 409, 521, 645, 942] [138, 282, 294, 410, 522, 646, 942] [139, 283, 295, 411, 523, 647, 942] [88, 132, 192, 480, 516, 620, 943] [89, 133, 193, 481, 517, 621, 943] [90, 134, 194, 482, 518, 622, 943] [91, 135, 195, 483, 519, 623, 943] [84, 128, 380, 420, 512, 752, 944] [85, 129, 381, 421, 513, 753, 944] [86, 130, 382, 422, 514, 754, 944] [87, 131, 383, 423, 515, 755, 944] [80, 124, 364, 388, 508, 600, 945] [81, 125, 365, 389, 509, 601, 945] [82, 126, 366, 390, 510, 602, 945] [83, 127, 367, 391, 511, 603, 945] [76, 120, 200, 504, 596, 628, 946] [77, 121, 201, 505, 597, 629, 946] [78, 122, 202, 506, 598, 630, 946] [79, 123, 203, 507, 599, 631, 946] [64, 108, 212, 492, 584, 616, 947] [65, 109, 213, 493, 585, 617, 947] [66, 110, 214, 494, 586, 618, 947] [67, 111, 215, 495, 587, 619, 947] [0, 1, 2, 3, 768, 802, 848] [4, 5, 6, 7, 786, 813, 836] [8, 9, 10, 11, 799, 835, 844] [12, 13, 14, 15, 775, 798, 834] [16, 17, 18, 19, 822, 833, 838] [20, 21, 22, 23, 772, 816, 832] [24, 25, 26, 27, 771, 818, 831] [28, 29, 30, 31, 782, 794, 830] [32, 33, 34, 35, 793, 812, 829] [36, 37, 38, 39, 828, 853, 857] [40, 41, 42, 43, 779, 809, 837] [44, 45, 46, 47, 808, 827, 855] [48, 49, 50, 51, 817, 825] [52, 53, 54, 55, 819, 824, 846] [56, 57, 58, 59, 769, 771, 823] [60, 61, 62, 63, 778, 822, 849] [64, 65, 66, 67, 821, 842, 850] [68, 69, 70, 71, 778, 803, 820] [72, 73, 74, 75, 801, 819, 845] [76, 77, 78, 79, 815, 818, 847] [80, 81, 82, 83, 768, 817, 846] [84, 85, 86, 87, 799, 826, 833] [88, 89, 90, 91, 824, 838, 841] [92, 93, 94, 95, 839, 854] [96, 97, 98, 99, 784, 840] [100, 101, 102, 103, 806, 808] [104, 105, 106, 107, 787, 805, 857] [108, 109, 110, 111, 780, 788] [112, 113, 114, 115, 797, 805, 856] [116, 117, 118, 119, 783, 796] [120, 121, 122, 123, 777, 785, 855] [124, 125, 126, 127, 784, 836, 854] [128, 129, 130, 131, 794, 828] [132, 133, 134, 135, 789, 840, 853] [136, 137, 138, 139, 773, 831, 852] [140, 141, 142, 143, 801, 841, 851] [144, 145, 146, 147, 776, 816, 850] [148, 149, 150, 151, 770, 843, 849] [152, 153, 154, 155, 835, 842, 848] [156, 157, 158, 159, 798, 824, 847] [160, 161, 162, 163, 772, 821, 846] [164, 165, 166, 167, 774, 791, 845] [168, 169, 170, 171, 773, 834, 844] [172, 173, 174, 175, 821, 843] [176, 177, 178, 179, 769, 842, 852] [180, 181, 182, 183, 770, 832, 841] [184, 185, 186, 187, 816, 831, 835] [188, 189, 190, 191, 815, 817, 849] [192, 193, 194, 195, 810, 814, 827] [196, 197, 198, 199, 789, 790, 796] [200, 201, 202, 203, 779, 788, 792] [204, 205, 206, 207, 781, 787, 807] [208, 209, 210, 211, 780, 786, 830] [212, 213, 214, 215, 785, 793, 840] [216, 217, 218, 219, 784, 809] [220, 221, 222, 223, 783, 804, 811] [224, 225, 226, 227, 782, 810, 829] [228, 229, 230, 231, 781] [232, 233, 234, 235, 780, 806, 814] [236, 237, 238, 239, 789, 807, 837] [240, 241, 242, 243, 779, 827, 830] [244, 245, 246, 247, 777, 787, 854] [248, 249, 250, 251, 776, 800, 826] [252, 253, 254, 255, 775, 825, 838] [256, 257, 258, 259, 774, 802, 852] [260, 261, 262, 263, 773, 803, 833] [264, 265, 266, 267, 772, 791, 823] [268, 269, 270, 271, 771, 822, 834] [272, 273, 274, 275, 770, 845, 848] [276, 277, 278, 279, 769, 800, 820] [280, 281, 282, 283, 778, 819, 825] [284, 285, 286, 287, 776, 791, 844] [288, 289, 290, 291, 802, 823, 826] [292, 293, 294, 295, 792, 795] [296, 297, 298, 299, 812, 839, 853] [300, 301, 302, 303, 811, 813, 814] [304, 305, 306, 307, 797, 810, 828] [308, 309, 310, 311, 804, 809] [312, 313, 314, 315, 808, 829, 857] [316, 317, 318, 319, 783, 786, 807] [320, 321, 322, 323, 795, 806, 856] [324, 325, 326, 327, 805, 839] [328, 329, 330, 331, 782, 792, 804] [332, 333, 334, 335, 813] [336, 337, 338, 339, 803, 815, 851] [340, 341, 342, 343, 768, 801, 850] [344, 345, 346, 347, 775, 800, 818] [348, 349, 350, 351, 799, 820, 847] [352, 353, 354, 355, 798, 843, 851] [356, 357, 358, 359, 777, 790, 797] [360, 361, 362, 363, 788, 796, 836] [364, 365, 366, 367, 795, 812, 855] [368, 369, 370, 371, 785, 794, 856] [372, 373, 374, 375, 781, 790, 793] [376, 377, 378, 379, 774, 832] [380, 381, 382, 383, 811, 837] [384, 385, 386, 387, 768, 773, 837] [388, 389, 390, 391, 768, 812, 836] [392, 393, 394, 395, 835, 838] [396, 397, 398, 399, 834, 846, 856] [400, 401, 402, 403, 801, 833, 855] [404, 405, 406, 407, 800, 832, 836] [408, 409, 410, 411, 825, 831] [412, 413, 414, 415, 789, 830, 835] [416, 417, 418, 419, 786, 829, 834] [420, 421, 422, 423, 811, 828, 833] [424, 425, 426, 427, 797, 832, 837] [428, 429, 430, 431, 796, 827, 831] [432, 433, 434, 435, 790, 825, 842] [436, 437, 438, 439, 787, 816, 824] [440, 441, 442, 443, 815, 823, 830] [444, 445, 446, 447, 768, 785, 822] [448, 449, 450, 451, 771, 783, 821] [452, 453, 454, 455, 770, 820, 829] [456, 457, 458, 459, 781, 819, 835] [460, 461, 462, 463, 818, 828] [464, 465, 466, 467, 789, 817, 852] [468, 469, 470, 471, 826, 827, 851] [472, 473, 474, 475, 777, 838, 850] [476, 477, 478, 479, 806, 825, 839] [480, 481, 482, 483, 824, 827, 840] [484, 485, 486, 487, 823, 854] [488, 489, 490, 491, 813, 822, 857] [492, 493, 494, 495, 785, 821] [496, 497, 498, 499, 809, 820, 856] [500, 501, 502, 503, 808, 819] [504, 505, 506, 507, 788, 818, 855] [508, 509, 510, 511, 795, 817, 854] [512, 513, 514, 515, 826] [516, 517, 518, 519, 814, 838, 853] [520, 521, 522, 523, 778, 792, 852] [524, 525, 526, 527, 791, 839, 851] [528, 529, 530, 531, 811, 834, 850] [532, 533, 534, 535, 802, 840, 849] [536, 537, 538, 539, 809, 833, 848] [540, 541, 542, 543, 832, 847, 857] [544, 545, 546, 547, 807, 831, 846] [548, 549, 550, 551, 799, 845] [552, 553, 554, 555, 806, 824, 844] [556, 557, 558, 559, 823, 843] [560, 561, 562, 563, 804, 822, 842] [564, 565, 566, 567, 776, 841, 854] [568, 569, 570, 571, 775, 813, 816] [572, 573, 574, 575, 774, 815, 853] [576, 577, 578, 579, 814, 852] [580, 581, 582, 583, 782, 790, 851] [584, 585, 586, 587, 788, 793, 850] [588, 589, 590, 591, 787, 849] [592, 593, 594, 595, 786, 848, 853] [596, 597, 598, 599, 779, 785, 847] [600, 601, 602, 603, 784, 846, 855] [604, 605, 606, 607, 783, 845, 857] [608, 609, 610, 611, 782, 807, 844] [612, 613, 614, 615, 781, 794, 843] [616, 617, 618, 619, 780, 840, 842] [620, 621, 622, 623, 789, 810, 841] [624, 625, 626, 627, 779, 790, 816] [628, 629, 630, 631, 777, 792, 815] [632, 633, 634, 635, 776, 798, 814] [636, 637, 638, 639, 775, 797, 821] [640, 641, 642, 643, 774, 788, 820] [644, 645, 646, 647, 773, 795, 819] [648, 649, 650, 651, 772, 786, 818] [652, 653, 654, 655, 771, 794, 817] [656, 657, 658, 659, 770, 784, 826] [660, 661, 662, 663, 769, 782, 849] [664, 665, 666, 667, 778, 793, 848] [668, 669, 670, 671, 780, 791, 847] [672, 673, 674, 675, 779, 802, 803] [676, 677, 678, 679, 776, 781, 792] [680, 681, 682, 683, 775, 780, 812] [684, 685, 686, 687, 774, 805, 811] [688, 689, 690, 691, 773, 783, 810] [692, 693, 694, 695, 772, 777, 809] [696, 697, 698, 699, 771, 808, 836] [700, 701, 702, 703, 770, 807, 828] [704, 705, 706, 707, 769, 784, 806] [708, 709, 710, 711, 778, 805] [712, 713, 714, 715, 787, 791, 804] [716, 717, 718, 719, 802, 813, 839] [720, 721, 722, 723, 803, 812, 845] [724, 725, 726, 727, 801, 844] [728, 729, 730, 731, 800, 810, 843] [732, 733, 734, 735, 799, 808, 841] [736, 737, 738, 739, 772, 798, 805] [740, 741, 742, 743, 797, 803, 804] [744, 745, 746, 747, 796, 801, 829] [748, 749, 750, 751, 795, 800] [752, 753, 754, 755, 794, 799, 837] [756, 757, 758, 759, 793, 798, 830] [760, 761, 762, 763, 769, 796] [764, 765, 766, 767, 856]
H_Z (552 checks, sparse supports)
[0, 80, 340, 384, 388, 444, 768] [1, 81, 341, 385, 389, 445, 768] [2, 82, 342, 386, 390, 446, 768] [3, 83, 343, 387, 391, 447, 768] [56, 176, 276, 660, 704, 760, 769] [57, 177, 277, 661, 705, 761, 769] [58, 178, 278, 662, 706, 762, 769] [59, 179, 279, 663, 707, 763, 769] [148, 180, 272, 452, 656, 700, 770] [149, 181, 273, 453, 657, 701, 770] [150, 182, 274, 454, 658, 702, 770] [151, 183, 275, 455, 659, 703, 770] [24, 56, 268, 448, 652, 696, 771] [25, 57, 269, 449, 653, 697, 771] [26, 58, 270, 450, 654, 698, 771] [27, 59, 271, 451, 655, 699, 771] [20, 160, 264, 648, 692, 736, 772] [21, 161, 265, 649, 693, 737, 772] [22, 162, 266, 650, 694, 738, 772] [23, 163, 267, 651, 695, 739, 772] [136, 168, 260, 384, 644, 688, 773] [137, 169, 261, 385, 645, 689, 773] [138, 170, 262, 386, 646, 690, 773] [139, 171, 263, 387, 647, 691, 773] [164, 256, 376, 572, 640, 684, 774] [165, 257, 377, 573, 641, 685, 774] [166, 258, 378, 574, 642, 686, 774] [167, 259, 379, 575, 643, 687, 774] [12, 252, 344, 568, 636, 680, 775] [13, 253, 345, 569, 637, 681, 775] [14, 254, 346, 570, 638, 682, 775] [15, 255, 347, 571, 639, 683, 775] [144, 248, 284, 564, 632, 676, 776] [145, 249, 285, 565, 633, 677, 776] [146, 250, 286, 566, 634, 678, 776] [147, 251, 287, 567, 635, 679, 776] [120, 244, 356, 472, 628, 692, 777] [121, 245, 357, 473, 629, 693, 777] [122, 246, 358, 474, 630, 694, 777] [123, 247, 359, 475, 631, 695, 777] [60, 68, 280, 520, 664, 708, 778] [61, 69, 281, 521, 665, 709, 778] [62, 70, 282, 522, 666, 710, 778] [63, 71, 283, 523, 667, 711, 778] [40, 200, 240, 596, 624, 672, 779] [41, 201, 241, 597, 625, 673, 779] [42, 202, 242, 598, 626, 674, 779] [43, 203, 243, 599, 627, 675, 779] [108, 208, 232, 616, 668, 680, 780] [109, 209, 233, 617, 669, 681, 780] [110, 210, 234, 618, 670, 682, 780] [111, 211, 235, 619, 671, 683, 780] [204, 228, 372, 456, 612, 676, 781] [205, 229, 373, 457, 613, 677, 781] [206, 230, 374, 458, 614, 678, 781] [207, 231, 375, 459, 615, 679, 781] [28, 224, 328, 580, 608, 660, 782] [29, 225, 329, 581, 609, 661, 782] [30, 226, 330, 582, 610, 662, 782] [31, 227, 331, 583, 611, 663, 782] [116, 220, 316, 448, 604, 688, 783] [117, 221, 317, 449, 605, 689, 783] [118, 222, 318, 450, 606, 690, 783] [119, 223, 319, 451, 607, 691, 783] [96, 124, 216, 600, 656, 704, 784] [97, 125, 217, 601, 657, 705, 784] [98, 126, 218, 602, 658, 706, 784] [99, 127, 219, 603, 659, 707, 784] [120, 212, 368, 444, 492, 596, 785] [121, 213, 369, 445, 493, 597, 785] [122, 214, 370, 446, 494, 598, 785] [123, 215, 371, 447, 495, 599, 785] [4, 208, 316, 416, 592, 648, 786] [5, 209, 317, 417, 593, 649, 786] [6, 210, 318, 418, 594, 650, 786] [7, 211, 319, 419, 595, 651, 786] [104, 204, 244, 436, 588, 712, 787] [105, 205, 245, 437, 589, 713, 787] [106, 206, 246, 438, 590, 714, 787] [107, 207, 247, 439, 591, 715, 787] [108, 200, 360, 504, 584, 640, 788] [109, 201, 361, 505, 585, 641, 788] [110, 202, 362, 506, 586, 642, 788] [111, 203, 363, 507, 587, 643, 788] [132, 196, 236, 412, 464, 620, 789] [133, 197, 237, 413, 465, 621, 789] [134, 198, 238, 414, 466, 622, 789] [135, 199, 239, 415, 467, 623, 789] [196, 356, 372, 432, 580, 624, 790] [197, 357, 373, 433, 581, 625, 790] [198, 358, 374, 434, 582, 626, 790] [199, 359, 375, 435, 583, 627, 790] [164, 264, 284, 524, 668, 712, 791] [165, 265, 285, 525, 669, 713, 791] [166, 266, 286, 526, 670, 714, 791] [167, 267, 287, 527, 671, 715, 791] [200, 292, 328, 520, 628, 676, 792] [201, 293, 329, 521, 629, 677, 792] [202, 294, 330, 522, 630, 678, 792] [203, 295, 331, 523, 631, 679, 792] [32, 212, 372, 584, 664, 756, 793] [33, 213, 373, 585, 665, 757, 793] [34, 214, 374, 586, 666, 758, 793] [35, 215, 375, 587, 667, 759, 793] [28, 128, 368, 612, 652, 752, 794] [29, 129, 369, 613, 653, 753, 794] [30, 130, 370, 614, 654, 754, 794] [31, 131, 371, 615, 655, 755, 794] [292, 320, 364, 508, 644, 748, 795] [293, 321, 365, 509, 645, 749, 795] [294, 322, 366, 510, 646, 750, 795] [295, 323, 367, 511, 647, 751, 795] [116, 196, 360, 428, 744, 760, 796] [117, 197, 361, 429, 745, 761, 796] [118, 198, 362, 430, 746, 762, 796] [119, 199, 363, 431, 747, 763, 796] [112, 304, 356, 424, 636, 740, 797] [113, 305, 357, 425, 637, 741, 797] [114, 306, 358, 426, 638, 742, 797] [115, 307, 359, 427, 639, 743, 797] [12, 156, 352, 632, 736, 756, 798] [13, 157, 353, 633, 737, 757, 798] [14, 158, 354, 634, 738, 758, 798] [15, 159, 355, 635, 739, 759, 798] [8, 84, 348, 548, 732, 752, 799] [9, 85, 349, 549, 733, 753, 799] [10, 86, 350, 550, 734, 754, 799] [11, 87, 351, 551, 735, 755, 799] [248, 276, 344, 404, 728, 748, 800] [249, 277, 345, 405, 729, 749, 800] [250, 278, 346, 406, 730, 750, 800] [251, 279, 347, 407, 731, 751, 800] [72, 140, 340, 400, 724, 744, 801] [73, 141, 341, 401, 725, 745, 801] [74, 142, 342, 402, 726, 746, 801] [75, 143, 343, 403, 727, 747, 801] [0, 256, 288, 532, 672, 716, 802] [1, 257, 289, 533, 673, 717, 802] [2, 258, 290, 534, 674, 718, 802] [3, 259, 291, 535, 675, 719, 802] [68, 260, 336, 672, 720, 740, 803] [69, 261, 337, 673, 721, 741, 803] [70, 262, 338, 674, 722, 742, 803] [71, 263, 339, 675, 723, 743, 803] [220, 308, 328, 560, 712, 740, 804] [221, 309, 329, 561, 713, 741, 804] [222, 310, 330, 562, 714, 742, 804] [223, 311, 331, 563, 715, 743, 804] [104, 112, 324, 684, 708, 736, 805] [105, 113, 325, 685, 709, 737, 805] [106, 114, 326, 686, 710, 738, 805] [107, 115, 327, 687, 711, 739, 805] [100, 232, 320, 476, 552, 704, 806] [101, 233, 321, 477, 553, 705, 806] [102, 234, 322, 478, 554, 706, 806] [103, 235, 323, 479, 555, 707, 806] [204, 236, 316, 544, 608, 700, 807] [205, 237, 317, 545, 609, 701, 807] [206, 238, 318, 546, 610, 702, 807] [207, 239, 319, 547, 611, 703, 807] [44, 100, 312, 500, 696, 732, 808] [45, 101, 313, 501, 697, 733, 808] [46, 102, 314, 502, 698, 734, 808] [47, 103, 315, 503, 699, 735, 808] [40, 216, 308, 496, 536, 692, 809] [41, 217, 309, 497, 537, 693, 809] [42, 218, 310, 498, 538, 694, 809] [43, 219, 311, 499, 539, 695, 809] [192, 224, 304, 620, 688, 728, 810] [193, 225, 305, 621, 689, 729, 810] [194, 226, 306, 622, 690, 730, 810] [195, 227, 307, 623, 691, 731, 810] [220, 300, 380, 420, 528, 684, 811] [221, 301, 381, 421, 529, 685, 811] [222, 302, 382, 422, 530, 686, 811] [223, 303, 383, 423, 531, 687, 811] [32, 296, 364, 388, 680, 720, 812] [33, 297, 365, 389, 681, 721, 812] [34, 298, 366, 390, 682, 722, 812] [35, 299, 367, 391, 683, 723, 812] [4, 300, 332, 488, 568, 716, 813] [5, 301, 333, 489, 569, 717, 813] [6, 302, 334, 490, 570, 718, 813] [7, 303, 335, 491, 571, 719, 813] [192, 232, 300, 516, 576, 632, 814] [193, 233, 301, 517, 577, 633, 814] [194, 234, 302, 518, 578, 634, 814] [195, 235, 303, 519, 579, 635, 814] [76, 188, 336, 440, 572, 628, 815] [77, 189, 337, 441, 573, 629, 815] [78, 190, 338, 442, 574, 630, 815] [79, 191, 339, 443, 575, 631, 815] [20, 144, 184, 436, 568, 624, 816] [21, 145, 185, 437, 569, 625, 816] [22, 146, 186, 438, 570, 626, 816] [23, 147, 187, 439, 571, 627, 816] [48, 80, 188, 464, 508, 652, 817] [49, 81, 189, 465, 509, 653, 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Code ID 948-24-28 · download JSON · raw on GitHub