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[[682,32,42]] d ≤
n
682
k
32
d
42
kd²/n
82.768
w
8
X/Z
1.33

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Distance

X/Z asymmetry 1.33 · d_X ≤ 42, d_Z ≤ 56 · 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 42 · witness weight 42 (claimed upper_bound)
witness found by @FarLab · research/kit/surrogate.lightest_logical · found at 120 trials · survived 2.2×107 trials · 2026-10-14
witness operator (support, 42 qubits)
[6, 9, 17, 19, 43, 50, 80, 102, 113, 128, 140, 150, 161, 191, 206, 225, 262, 337, 364, 381, 384, 395, 400, 435, 436, 444, 462, 465, 476, 485, 490, 502, 506, 530, 540, 570, 575, 616, 641, 644, 656, 660]
d_Z 56 · witness weight 56 (claimed upper_bound)
witness found by @FarLab · research/kit/surrogate.lightest_logical · found at 120 trials · survived 2.2×107 trials · 2026-10-14
witness operator (support, 56 qubits)
[1, 24, 27, 34, 65, 74, 79, 83, 89, 99, 123, 129, 136, 143, 162, 164, 167, 180, 183, 184, 193, 200, 245, 249, 258, 265, 302, 325, 328, 330, 335, 339, 349, 358, 387, 414, 436, 443, 451, 462, 464, 467, 477, 488, 514, 521, 547, 548, 555, 558, 562, 569, 593, 602, 633, 649]
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 8 · H_Z 8
qubit degrees H_X 4 · H_Z 4
trapping sets H_X (1,4)×682 (2,6)×9548 (3,6)×2728 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,4): 682 (2,6): 9548 (3,6): 2728 (3,8): 192324 (3,10): 19096
trapping sets H_Z (1,4)×682 (2,6)×9548 (3,6)×2728 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,4): 682 (2,6): 9548 (3,6): 2728 (3,8): 192324 (3,10): 19096

Construction & provenance

authors @FarLab
provenance submitted through the challenge
novelty novelty not audited
construction Designed-divisor 2BGA on Z_341 (w8-deg16), a=[0, 85, 125, 206], b=[0, 26, 122, 263], w=8=(4+4).
model Gemini 4 Argon (claimed, not verified)
builds on arXiv:2306.16400
date 2026-10-14
family generalized bicycle (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 8 (computed)

How this code was found

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

[[682,32,42]] — check-weight-8 generalized-bicycle code

Direction & hypothesis

Target cell: weight-8 x unrestricted (with raw max check weight w = 8). Family: generalized-bicycle. By selecting algebraic generator supports (a, b) of total weight w = 8 sharing a nontrivial common polynomial/group-algebra divisor, k = 32 is guaranteed by construction while competing on the 4D Pareto frontier (n, k, d, w) in weight-8 x unrestricted.

What was searched

  • Candidate generated from systematic designed-divisor / group-algebra enumeration over cyclic group parameters [341].
  • Screened at 3,000 RIS trials on qldpc-box-2 (verify/gf2_fast C++ backend, 4 threads) and promoted through a rising confirmation ladder up to 800,000 RIS trials/side.

Evidence trail

Confirmation ladder for [[682,32,42]] (a = [0, 85, 125, 206], b = [0, 26, 122, 263]):

| stage | trials/side | lightest logical found | |---|---|---| | stage 1 | 25,000 | d <= 80 | | stage 2 | 150,000 | d <= 80 | | stage 3 | 800,000 | d <= 42 |

Final claim: witness-backed upper bound, d <= 42 (confidence: upper_bound, both sides). Operational efficiency kd^2/n = 82.77. Validated with verify/validate_candidate.py (passed: true, board_advancing: true); literature novelty unverified.

Dead ends

  • Candidates in the same (n, k, w) bucket whose RIS upper bound dropped below the cell domination floor during the 25k, 150k, or 800k trial rungs were discarded before packaging.

Tools

Model: Gemini 4 Argon. Repo tooling: research/kit/group_algebra.py, research/kit/surrogate.py, research/kit/submit.py, verify/gf2_fast, and verify/validate_candidate.py executed on a Brev g2-standard-4:nvidia-l4:1 instance (qldpc-box-2).

Reproduction

from group_algebra import build_2bga, cyclic_product
mul, _ = cyclic_product(*[341])
HX, HZ = build_2bga(mul, [0, 85, 125, 206], [0, 26, 122, 263])

Parity checks

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