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[[730,28,38]] d ≤
n
730
k
28
d
38
kd²/n
55.386
w
8
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 38, d_Z ≤ 38 · 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 38 · witness weight 38 (claimed upper_bound)
witness found by @vprusso · GPU deep kernel (full basis, pair depth 8) · found at 2×107 trials · survived 1.8×108 trials · 2026-09-23
witness operator (support, 38 qubits)
[0, 15, 18, 51, 54, 76, 89, 110, 113, 153, 157, 242, 248, 288, 347, 372, 397, 404, 413, 416, 429, 438, 457, 460, 469, 475, 500, 501, 510, 541, 572, 609, 610, 635, 641, 650, 669, 707]
d_Z 38 · witness weight 38 (claimed upper_bound)
witness found by @vprusso · GPU sketch k_sub 256 (recover), screen stage 3 · found at 5×106 trials · survived 1.8×108 trials · 2026-09-23
witness operator (support, 38 qubits)
[16, 47, 78, 87, 88, 110, 119, 131, 150, 159, 172, 175, 184, 191, 216, 246, 284, 303, 312, 318, 340, 343, 344, 381, 431, 435, 453, 475, 499, 512, 534, 537, 570, 573, 588, 665, 705, 711]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 8 · H_Z 8
qubit degrees H_X 4 · H_Z 4
trapping sets H_X (1,4)×730 (2,4)×365 (3,6)×14600 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,4): 730 (2,4): 365 (2,6): 9490 (3,6): 14600 (3,8): 175930 (3,10): 16060
trapping sets H_Z (1,4)×730 (2,4)×365 (3,6)×14600 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,4): 730 (2,4): 365 (2,6): 9490 (3,6): 14600 (3,8): 175930 (3,10): 16060

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty new parameter set claimed by submitter
construction Cyclic (single-circulant-pair) generalized-bicycle code over Z_365 (research/cyclic_gb.py build_cyclic_gb): a(x) = 1 + x25 + x97 + x237, b(x) = 1 + x3 + x138 + x350; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with circ(v)[i, (i + j) mod 365] = v[j]. n = 2m = 730, k = 2 deg gcd(a, b, x365 - 1) = 28, every check has weight 8. a and b were drawn as weight-4 multiples of a degree-13 divisor g of x365 - 1 (g as a little-endian bit integer: 8479).
model Claude Claude Fable 5.1 (Claude Code) (claimed, not verified)
builds on arXiv:1212.6703, arXiv:2111.03654
date 2026-09-23
notes Found by a GPU random-information-set screen (deep kernel: full-basis RREF plus pair sums) over cyclic generalized-bicycle codes with weight-4 polynomials at n in [702, 1000]; see the research note for the ladder. Lightest logicals: X 38, Z 38; deep-kernel GPU passes (full basis, pair depth 8): X 38 at 20,000,000 trials (seed 2101); Z 40 at 20,000,000 trials (seed 2101); X 38 at 100,000,000 trials (seed 2102); Z 38 at 100,000,000 trials (seed 2102); board fast pass 40 at 8,000,000 trials. Every operator re-verified with verify/gf2.py. Distance is a witness-backed upper bound. Novelty: no isomorphic code found by a nauty canonical-form check against the board and the 2BGA, GB, BB, QECDB, and codetables data (submitter claim). Generator spec: {"family": "cyclic-gb", "m": 365, "g_int": 8479, "deg_g": 13, "a": [0, 25, 97, 237], "b": [0, 3, 138, 350]}
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

[[730,28,38]] cyclic generalized-bicycle code over Z_365 (single circulant pair)

Direction & hypothesis

Cell: unrestricted x weight-8, the extended tier n in (700, 1000] with w <= 8 and d <= 40 (base tier for n <= 700). The cell's weight-8 frontier above n = 684 holds only the pair-partition CPM codes at d <= 20 and the planar tiles at k = 18; nothing with k in [21, 200] has d > 24 at n <= 1000, so a code with k in the twenties or forties and d in the thirties is a strict Pareto record even though it cannot reach the cell's kd^2/n headline (106.1, [[684,14,72]]; that regime is closed above n = 700 by the d <= 40 rule, and k <= 20 is dominated by [[684,20,48]]). The hypothesis was that cyclic generalized-bicycle codes with weight-4 supports keep distance in the thirties at n = 700 to 1000 once k is forced above 20 by construction.

What was searched

  • Cyclic GB over odd m in [351, 500] (n = 2m in [702, 1000]): a divisor g of x^m - 1 of degree 11 to 26 is chosen at random from the irreducible factors (sympy over GF(2)), then every weight-4 multiple of g mod x^m - 1 containing x^0 is enumerated by a meet-in-the-middle over the residues x^i mod g, and pairs (a, b) from distinct rotation classes are built with research/cyclic_gb.py build_cyclic_gb. k = 2 deg gcd(a, b, x^m - 1) is at least 2 deg g; pairs with k > 2 deg g + 6 (a and b sharing more than g) were dropped, since their distance is 2 to 7.
  • 336 such pairs were built in the stream that produced this code (seed 13, batches of 48); 140 passed the exact-k filter, 26 survived the first GPU stage, 25 the third. 387,200,000 GPU sketch trials in total.
  • The GPU screen is verify/ris_gpu.cu (the sqetch random-sketch RIS kernel) driven through verify/ris_gpu.py's packing, in three stages per side: 300,000 trials at a 64-row sketch (estimate mode, early stop below the record threshold), 2,000,000 at a 256-row sketch, then 5,000,000 in recover mode; every recovered operator is re-verified with verify/gf2.py (in the kernel of the opposite checks, outside the row space of its own checks) before it counts.
  • Record thresholds were computed against the board checkout at the time

    • (dominance over n down, k up, d up, w down); a candidate was dropped as soon as any side showed a logical lighter than the smallest record-making d for its (n, k, w), which is sound because RIS weights are upper bounds.

Evidence trail

Every operator in the table was re-verified on the CPU with verify/gf2.py (zero syndrome against the opposite checks, outside the row space of its own checks, weight recounted) before it was recorded. Weights are the lightest found by that run.

| instrument | side | trials | seed | lightest logical | |---|---|---:|---:|---:| | screen stage 1, GPU sketch, k_sub 64 | X | 300,000 | 13000006029 | 99 | | screen stage 1, GPU sketch, k_sub 64 | Z | 300,000 | 13000006030 | 74 | | screen stage 2, GPU sketch, k_sub 256 | X | 2,000,000 | 13000006306 | 40 | | screen stage 2, GPU sketch, k_sub 256 | Z | 2,000,000 | 13000006307 | 46 | | screen stage 3, GPU sketch (recover), k_sub 256 | X | 5,000,000 | 13000006606 | 40 | | screen stage 3, GPU sketch (recover), k_sub 256 | Z | 5,000,000 | 13000006607 | 38 | | gf2_fast CPU RIS, pair depth 8, 4 threads, both sides | X | 200,000 | 876 | 40 | | finalist GPU sketch, k_sub 256 | X | 50,000,000 | 777 | 40 | | finalist GPU sketch, k_sub 256 | Z | 50,000,000 | 778 | 38 | | GPU deep kernel, full basis, pair depth 8 | X | 20,000,000 | 2101 | 38 | | GPU deep kernel, full basis, pair depth 8 | Z | 20,000,000 | 2101 | 40 | | GPU deep kernel, full basis, pair depth 8 | X | 100,000,000 | 2102 | 38 | | GPU deep kernel, full basis, pair depth 8 | Z | 100,000,000 | 2102 | 38 | | board fast pass, gf2_fast pair depth 8, 3 threads, both sides | both | 8,000,000 | 2209 | 40 |

Board CPU gate (verify/validate_candidate.py, then verify/gate_changed.py's structural and fast passes, run out of CI on the candidate file):

  • first pass (fast pass wall-clock capped at 30 minutes): validate_candidate passed = True (its 8000-trial pure-Python refute_check found nothing lighter); circulant-GB structural pass: lightest single-block logical 73 at 400,000 trials; gf2_fast fast pass: lightest logical 40 at 3,510,000 trials (1801 s).
  • full pass (8,000,000-trial fast pass, uncapped): validate_candidate passed = True (its 8000-trial pure-Python refute_check found nothing lighter); circulant-GB structural pass: lightest single-block logical 73 at 400,000 trials; gf2_fast fast pass: lightest logical 40 at 8,000,000 trials (8606 s).

Claim: witness-backed upper bound d <= 38 (X <= 38, Z <= 38), not exact. The lightest logical did not move between the 5,000,000-trial screen stage, the 50,000,000-trial sketch pass, and the deep-kernel passes listed above.

Dead ends

  • Random weight-8 bivariate bicycle codes at n in [702, 1000]: k >= 21 in

    • 1 of 623 built codes; 29,716 draws gave 3 stage-3 survivors ([[980,28,35]] and [[784,22,28]] at the 5,000,000-trial sketch stage, not taken further).

  • Dihedral 2BGA with |a| = |b| = 4, n in [704, 1000]: 81,300 draws, k >= 21

    • in 526, none survived the first GPU stage (every one had a logical lighter than 25).

  • Cyclic GB pairs sharing more than the designed divisor (k = 100 to 496)

    • have d = 2 to 7; pairs whose offsets share a factor with m are direct sums.

  • GPU sketch bounds on high-rate codes inflate badly: pair-partition CPM

    • draws reading 22 to 24 at 20,000,000 sketch trials came out at 18 to 20 under a full-basis search. On the low-rate codes in this note the sketch and the full-basis instruments agree.

Tools

Model: Claude Fable 5.1 (Claude Code), matching provenance.model. Generators from research/kit (search.py samplers, group_algebra.py) and research/cyclic_gb.py; GPU RIS from verify/ris_gpu.cu built with nvcc for an NVIDIA A40, driven through verify/ris_gpu.py's input format; gf2_fast from verify/ for exact k, kernels, and the CPU RIS; verify/validate_candidate.py and verify/gate_changed.py for the gate. Compute: about 3.5 GPU hours for the stream that produced this code plus about 1 GPU hour of finalist passes, and about 4 CPU hours of gate runs.

Reproduction

Rebuild (H_X, H_Z) from the construction string in the code file's provenance: Cyclic (single-circulant-pair) generalized-bicycle code over Z_365 (research/cyclic_gb.py build_cyclic_gb): a(x) = 1 + x^25 + x^97 + x^237, b(x) = 1 + x^3 + x^138 + x^350; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with circ(v)[i, (i + j) mod 365] = v[j]. n = 2m = 730, k = 2 deg gcd(a, b, x^365 - 1) = 28, every check has weight 8. a and b were drawn as weight-4 multiples of a degree-13 divisor g of x^365 - 1 (g as a little-endian bit integer: 8479).

Parity checks

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