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[[630,20,24]] d ≤
n
630
k
20
d
24
kd²/n
18.286
w
6
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 24, d_Z ≤ 24 · w_X = 6, w_Z = 6 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 24 · witness weight 24 (claimed upper_bound)
witness found by @vprusso · GPU deep kernel (full basis, pair depth 8), screen stage 3 · found at 2×106 trials · survived 6×107 trials · 2026-09-23
witness operator (support, 24 qubits)
[16, 19, 47, 176, 207, 210, 238, 244, 253, 269, 272, 275, 278, 281, 284, 287, 300, 320, 390, 437, 465, 537, 565, 607]
d_Z 24 · witness weight 24 (claimed upper_bound)
witness found by @vprusso · GPU deep kernel (full basis, pair depth 8), screen stage 3 · found at 2×106 trials · survived 6×107 trials · 2026-09-23
witness operator (support, 24 qubits)
[62, 77, 82, 107, 152, 162, 177, 222, 252, 277, 307, 327, 330, 361, 540, 543, 546, 549, 552, 574, 583, 608, 611, 614]
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 6 · H_Z 6
qubit degrees H_X 3 · H_Z 3
trapping sets H_X (1,3)×630 (2,4)×4725 (3,3)×630 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 630 (2,4): 4725 (3,3): 630 (3,5): 45360 (3,7): 6300
trapping sets H_Z (1,3)×630 (2,4)×4725 (3,3)×630 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 630 (2,4): 4725 (3,3): 630 (3,5): 45360 (3,7): 6300

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_315 (research/cyclic_gb.py build_cyclic_gb): a(x) = 1 + x70 + x215, b(x) = 1 + x3 + x284; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with circ(v)[i, (i + j) mod 315] = v[j]. n = 2m = 630, k = 2 deg gcd(a, b, x315 - 1) = 20, every check has weight 6. a and b were drawn as weight-3 multiples of a degree-10 divisor g of x315 - 1 (g as a little-endian bit integer: 1269).
model Claude Claude Fable 5.1 (Claude Code) (claimed, not verified)
builds on arXiv:1904.02703, arXiv:2203.17216
date 2026-09-23
notes Found by a GPU random-information-set screen (verify/ris_gpu.cu deep kernel: full-basis RREF plus pair sums, pair depth 8) over weight-6 cyclic generalized-bicycle codes with weight-3 polynomials at n <= 700; see the research note for the ladder. Lightest logicals: X 24, Z 24; finalist deep-kernel GPU pass: X 24 at 50,000,000 trials (seed 777); Z 24 at 50,000,000 trials (seed 778); board fast pass 24 at 8,000,000 trials. Every operator re-verified with verify/gf2.py. Distance is a witness-backed upper bound. Novelty: new_parameters by a nauty canonical-form check of the typed Tanner graph against the board and the 2BGA, GB, BB, QECDB, and codetables data (a submitter claim). Generator spec: {"family": "cyclic-gb", "m": 315, "g_int": 1269, "deg_g": 10, "a": [0, 70, 215], "b": [0, 3, 284]}
family generalized bicycle (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 6 (computed)

How this code was found

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

[[630,20,24]] weight-6 cyclic generalized-bicycle code over Z_315 (single circulant pair)

Direction & hypothesis

Cell: unrestricted x weight-6, base tier (n <= 700, no distance cap). The weight-6 cell holds few codes: its headline is [[672,20,32]] at kd^2/n 30.5 and below it sit [[630,12,34]], [[630,14,30]], [[576,12,30]], [[510,16,24]], [[540,12,28]], and [[360,12,24]], all at kd^2/n 18 to 22, then a long tail under 16. The hypothesis was that weight-3 polynomials in the bicycle families (cyclic GB, BB, 2BGA) still reach distances in the twenties and thirties at n = 200 to 700 once k is forced above 8, so that a strict Pareto record with kd^2/n above 12 is available in the band between those incumbents; the cell headline (30.5) was the stretch target.

What was searched

  • Cyclic GB over odd m in [101, 349] (n = 2m in [202, 698]): a divisor g of x^m - 1 of degree 5 to 24 is chosen at random from the irreducible factors (sympy over GF(2)), every weight-3 multiple of g mod x^m - 1 containing x^0 is enumerated (residues x^i mod g, one lookup per pair), and pairs (a, b) from distinct rotation classes with gcd(offsets, m) = 1 are built with research/cyclic_gb.py build_cyclic_gb. k = 2 deg gcd(a, b, x^m - 1) >= 2 deg g; pairs with k > 2 deg g + 6 were dropped.
  • 12,288 draws in the stream that produced this code; 11,951 passed the prefilter (CSS, exact k with gf2_fast, an eff floor of 12 on kd^2/n, and a strict-record threshold against the board checkout), 321 survived the first GPU stage, 263 the third. 2,610,200,000 GPU deep-kernel trials in total, 2.40 GPU hours busy on one NVIDIA A40.
  • Screen: verify/ris_gpu.cu's deep kernel (full-basis RREF plus pair sums, pair depth 8) in three stages per side, 100,000, 500,000, and 2,000,000 trials, with early stop as soon as a logical lighter than the record threshold appears (sound, since RIS weights are upper bounds). Every recovered operator is re-verified with verify/gf2.py before it counts.
  • Record thresholds were computed against the board checkout at origin/main

    • 110d467f (dominance over n down, k up, d up, w down, with equal parameters counting as dominated), plus a floor kd^2/n >= 12; a candidate was dropped as soon as any side showed a logical lighter than the smallest record-making d for its (n, k, w).

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 (estimate) | X | 100,000 | 71000011009 | 24 | | screen stage 2 (estimate) | X | 500,000 | 71000011304 | 24 | | screen stage 3 (recover) | X | 2,000,000 | 71000011604 | 24 | | screen stage 1 (estimate) | Z | 100,000 | 71000011010 | 24 | | screen stage 2 (estimate) | Z | 500,000 | 71000011305 | 24 | | screen stage 3 (recover) | Z | 2,000,000 | 71000011605 | 24 | | gf2_fast CPU RIS, pair depth 8, 1 thread, both sides | X | 200,000 | 876 | 24 | | finalist GPU deep kernel, full basis, pair depth 8 | X | 50,000,000 | 777 | 24 | | finalist GPU deep kernel, full basis, pair depth 8 | Z | 50,000,000 | 778 | 24 | | board fast pass, gf2_fast pair depth 8, 2 threads, both sides | both | 8,000,000 | 5259 | 24 |

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, laptop, 2 threads): validate_candidate passed = True (labels ['advances the weight-6 x unrestricted board', 'literature novelty UNVERIFIED']); circulant-GB structural pass lightest single-block logical 26 at 400,000 trials; gf2_fast fast pass lightest logical 24 at 8,000,000 trials (2566 s, 2 threads, seed 5259); GATE passed.

Claim: witness-backed upper bound d <= 24 (X <= 24, Z <= 24), not exact. The lightest logical did not move between the 2,000,000-trial screen stage, the 200,000-trial CPU pass, the 50,000,000-trial deep-kernel pass per side, and the board's 8,000,000-trial fast pass.

Dead ends

  • Cyclic GB with weight-3 polynomials: 12,288 draws over m in [101, 349]

    • gave 263 stage-3 survivors, but only 13 distinct (n, k) parameter sets, because weight-3 multiples of a divisor exist only for a few m (105, 127, 147, 155, 217, 231, 255, 279, 315, 341) and k is pinned at 2 deg g = 10 to 20; nothing reached kd^2/n 30.5, and the [[682,10,38]] and [[682,10,36]] screen survivors (kd^2/n 21.2, 19.0) fell to 34 under the board's gf2_fast pass and the finalist pass, where [[630,12,34]] dominates them.

  • Weight-3 BB: 123,744 draws, k = 0 in 94 percent; the k >= 6 survivors are

    • low-rate codes at d 32 to 42 with kd^2/n 12 to 17.

  • Metacyclic and dihedral 2BGA with |a| = |b| = 3: k = 0 for most draws

    • (71 percent of metacyclic draws); two metacyclic survivors in 0.4 GPU hours; the dihedral stream did not run (the pod's GPU was needed by another session).

  • Ties: the same construction reproduces the board's [[254,14,16]] and

    • [[510,16,24]] parameter sets repeatedly; those are not records and were filtered out.

Tools

Generators from research/kit (search.py samplers, bb.py, group_algebra.py) and research/cyclic_gb.py; GPU RIS from verify/ris_gpu.cu built with nvcc for an NVIDIA A40 (blocking-sync host thread), 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; a nauty canonical-form check of the typed Tanner graph (pynauty, outside this repo) for the novelty label. Model: Claude Fable 5.1 (Claude Code), matching provenance.model. Compute: about 2.4 GPU hours for the stream that produced this code, about 0.15 GPU hours for the finalist pass, and about 1 CPU hour for the gate.

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_315 (research/cyclic_gb.py build_cyclic_gb): a(x) = 1 + x^70 + x^215, b(x) = 1 + x^3 + x^284; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with circ(v)[i, (i + j) mod 315] = v[j]. n = 2m = 630, k = 2 deg gcd(a, b, x^315 - 1) = 20, every check has weight 6. a and b were drawn as weight-3 multiples of a degree-10 divisor g of x^315 - 1 (g as a little-endian bit integer: 1269).

Parity checks

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