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[[630,12,34]] d ≤
n
630
k
12
d
34
kd²/n
22.019
w
6
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 34, d_Z ≤ 34 · 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 34 · witness weight 34 (claimed upper_bound)
witness found by @dorakingx · gf2_fast RIS (verify/gf2_fast.cpp), both sides searched jointly · found at 2×105 trials · survived 5×106 trials · 2026-09-05
witness operator (support, 34 qubits)
[14, 42, 48, 74, 87, 100, 126, 139, 180, 185, 191, 219, 225, 250, 264, 271, 337, 449, 483, 491, 498, 499, 503, 505, 507, 508, 509, 510, 511, 512, 513, 573, 580, 581]
d_Z 34 · witness weight 34 (claimed upper_bound)
witness found by @dorakingx · mirror of the other side's witness (L(e)<->R(-e)); sides searched jointly · found at 2×105 trials · survived 5×106 trials · 2026-09-05
witness operator (support, 34 qubits)
[49, 50, 57, 117, 118, 119, 120, 121, 122, 123, 125, 127, 131, 132, 139, 147, 181, 293, 359, 366, 380, 405, 411, 439, 445, 450, 491, 504, 530, 543, 556, 582, 588, 616]
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 @dorakingx
provenance submitted through the challenge
novelty novelty not audited
construction Generalized bicycle (two-block) code on Z_315: H_X=[A|B], H_Z=[B^T|A^T] with A, B the 315x315 circulants of a(x)=1+x+x8, b(x)=1+x52+x229 (circulant row u touches qubits u-e mod 315 for each exponent e; right block index offset 315). k = 2*deg gcd(a, b, x315-1) = 12. Found by exhaustive designed-divisor enumeration of all weight-6 trinomial pairs on Z_N, N=181..350 (k >= 8; 109,888 listed pairs = 102,092 classes under monomial factors, units and swap), then fresh-seed fast-RIS ladders; the distance is a witness-backed upper bound (deepest null result 5000000 trials).
model Claude Claude Fable 5.1 (Claude Code) (claimed, not verified)
builds on arXiv:1904.02703, arXiv:2203.17216, arXiv:2306.16400, arXiv:2503.03827
date 2026-09-05
notes Checked, not equivalent to any board entry: no board entry has n=630 with k=12 (the two n=630 entries, [[630,86,3]] w=4 and [[630,126,20]] w=9, are not weight-6 codes); closed-walk counts of the Tanner graph differ from every weight-6 board entry and the gate reports no exact duplicate (WL cannot separate circulant codes). The Z witness is the image of the X witness under the two-block symmetry L(e)<->R(-e); the RIS runs searched both sides jointly. Literature novelty unverified.
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

[[630,12,34]] — weight-6 generalized bicycle code on Z_315 from an exhaustive designed-divisor enumeration

Direction & hypothesis

Target cell: unrestricted × weight-6, whose leader is the twisted-torus BB code [[360,12,24]] (kd²/n = 19.2, an upper bound) from arXiv:2503.03827. That paper's exhaustive twisted-torus search stopped at n ≤ 400. Above n = 400 the cell's entries with kd²/n > 10 were [[510,16,24]] (a member of the known [[2^(m+1)−2, 2m]] GB family, 18.1), [[540,12,28]] (a metacyclic 2BGA support-mutation search, 17.4), [[682,20,22]] (an orbit-structured GB search, 14.2) and [[450,8,26]] (spectral-k screened BB, 12.0); the k = 2 GB entries ([[422,2,31]], [[454,2,33]]) and the many low-d local and product entries sit far lower. None reaches 19.2. Two observations made the region 360 < n ≤ 700 a finite target: 29 of the 39 twisted-torus codes seeded on the board have a cyclic group Z²/L, i.e. they are ordinary generalized bicycle (GB) codes (Panteleev–Kalachev arXiv:1904.02703; Wang–Pryadko arXiv:2203.17216; Lin–Pryadko arXiv:2306.16400), and for a cyclic group the logical count is exact and free, k = 2·deg gcd(f, g, X^N − 1). So the cyclic part of the family can be enumerated completely by designed divisor (the mechanism of fieldnotes/2026-07-14-designed-divisor-and-odd-k.md) for every N = 181..350, without building a matrix or sampling.

What was searched

All weight-6 trinomial pairs f = 1 + X^e1 + X^e2, g = 1 + X^e3 + X^e4 on Z_N, N = 181..350, with k ≥ 8, reduced modulo monomial factors, the unit group Z_N^* (relabelling automorphisms, including inversion) and the f↔g swap: 109,888 listed pairs, an exhaustive superset of a transversal (the on-the-fly reduction misses duplicates when f or g has a nontrivial unit stabiliser); an exact recount gives 102,092 classes (k = 8: 69,866; 10: 26,126; 12: 4,300; 14: 1,035; 16: 591; 18–36: 174). Only 17 values of N admit k ≥ 12 at all. X^N − 1 was factored once per N and divisibility of a trinomial by each factor power is three table lookups, so a full N takes 10–60 s. Every k ≥ 10 pair was screened at 120 fast-RIS trials (the repo's gf2_fast backend). Ladder rungs used a fresh seed each and pair depth 12–32; candidates were dropped when their upper-bound kd²/n fell below 19.2, and the rungs were also rank-truncated by compute: k ≥ 12: top 500 at 2k, 325 run at 20k (167 still above 19.2), top 60 at 200k, 18 at 1M, 6 at 2M (three [[630,12]], three [[630,14]]), 2 at 5M; k = 10: 800 pairs at 2k, 430 run at 20k (274 still above 19.2), 40 at 200k (20 of them promoted straight from the screen ranking), 10 at 1M, then 2M on the seven still above 19.2 and 5M on four (see Evidence trail). Rung counts are per laddered listing; the listing is a superset of a transversal, so a few classes appear twice. The 74,618 listed k = 8 pairs were enumerated but not distance-screened (k = 8 needs d ≥ 39 at n = 630 to beat the bar). A non-cyclic twisted-torus sweep (29 of the 31 distinct seeded polynomial shapes × all 5,507 non-cyclic lattices of index 181..350) and the (3,3)-BB shape on all 74,063 lattices were run alongside.

Evidence trail

Submitted code: f = 1 + x + x⁸, g = 1 + x⁵² + x²²⁹ on Z_315, n = 630, k = 12. Fresh-seed fast-RIS ladder, lightest logical found (trials per rung): 42 @120 → 42 @2k → 38 @20k → 34 @200k → 34 @1M → 34 @2M (pair depth 24) → 34 @5M (pair depth 32); seven independent seeds, ~8.2M trials in total, nothing lighter than 34 ever seen. The X-witness of weight 34 is the one found at 200k trials; the Z witness is its image under the block-swap/inversion symmetry of two-block codes (L(e) ↔ R(−e)), re-verified by the GF(2) stack (the RIS runs search both sides jointly, so the Z side carries the same null-result budget). A separate fresh-seed run of verify/heuristic_distance.py during the author's own pre-submission review (same machine; 3M accelerator trials, seed 20260905) returned 34, "corroborated". Claim: **d ≤ 34, upper bound**; not exact. Gate verdict (verify/validate_candidate.py): passed, not refuted, "advances the weight-6 x unrestricted board", "literature novelty UNVERIFIED".

Siblings (distinct codes under the unit/shift/swap group, and separated by closed-walk counts of the Tanner graph; the verifier's WL signature cannot separate circulant codes): fifteen distinct [[630,12]] codes read 34 at 200k (tally per laddered listing); of the thirteen taken to 1M, two held 34 (this code and f = 1+x+x⁶⁹, g = 1+x¹⁵+x²¹², both also holding at 2M and 5M), eight fell to 32 (kd²/n 19.5) and three to 30; two were not laddered further. A pair that read 36 at 200k (f = 1+x+x²⁵, g = 1+x⁴⁰+x²⁵⁷) fell 36 → 34 → 32. All three [[630,14]] pairs that read 32 at 200k fell to 30 at 1M and held 30 at 2M (kd²/n 20.0; Pareto points not submitted here, left as open leads). k = 10 (n = 682 needs d ≥ 37): 274 pairs above 19.2 at 20k, 40 run at 200k, 10 at 1M, after which the seven still above 19.2 went to 2M (pair depth 24, one of them in an earlier pass; the [[682,10,≤40]] read 38) and four to 5M (pair depth 32): only f = 1+x+x⁵¹, g = 1+x¹⁰+x²³³ still read 38 there, and the others fell to 36 or 34. Correction (2026-09-10): that survivor falls too. A fresh-seed ladder on it returns a valid weight-36 logical at 20M trials (seed 990001), verified against the opposite-type checks and outside the same-type row space; a second [[682,10]] pair (f = 1+x+x⁴³, g = 1+x¹⁷+x⁶⁶) falls the same way at 5M. So k = 10 at N = 341 tops out at [[682,10,≤36]], kd²/n 19.0 — below the 19.2 this note quotes as the bar, not the 21.2 it claimed. Nothing at k = 10 in this family is a Pareto point above that bar. That 200k → 1M → 2M attrition is the calibration warning of this family: a value flat across 20k → 200k is not converged at n = 630, and 34 for this code is an upper bound that seven seeds and 8.2M trials failed to lower, not a proof.

BP+OSD cross-check (decode/distance.py, 100k injections of weight ⌈d/2⌉..+2, 553 s under a 900 s cap): the pinned decoder corrected every injected error, no nontrivial residual at all — inconclusive, adds no evidence at this size.

Literature novelty is unverified: the exhaustive GB tables of arXiv:2203.17216 (k = 2 families at prime circulant sizes) and the 2BGA enumeration of arXiv:2306.16400 (n ≤ 100 for abelian groups) do not reach weight 6, k = 12 at N = 315, and no further literature check was made.

Dead ends

  • The (3,3)-BB shape (f = 1+x+x⁻¹y³, g = 1+y+x³y⁻¹, the gross / [[360,12,24]]

    • polynomials) on every lattice of index 181..350: best [[696,8]] 56 @120 → 42 @2k → 40 @20k, kd²/n 18.4; [[648,12]] 38 → 28. Nothing above 19.2.

  • k = 12 GB pairs at N = 336 ([[672,12]]): 46 @2k → 38 @20k → 28 @200k.
  • Non-cyclic twisted tori (29 shapes × 5,507 lattices): screen leaders

    • [[700,6,≤76]], [[600,8,≤60]] collapsed; at 200k the best was [[630,8,≤40]] (kd²/n 20.3, k = 8 needs d ≥ 39 to stay above the bar and was not taken deeper), [[630,10]] fell 38 → 32, [[686,6]] 48 → 46.

  • 2D-local layouts: no bilayer layout was found. In the author's layout

    • tool (not part of this PR) the submitted code's best twisted-torus presentation has check-shape diameter 8.3 (siblings 4.6–7.4), against 3.06 for [[360,12,24]], whose folded two-layer layout on the board reaches r = 6.93; folding multiplies the diameter by roughly 2, so r ≤ 7 is out of reach here.

Tools

Claude Fable 5.1 (Claude Code) as the agent; numpy constructor + bit-packed GF(2) rank; sympy for the factorisation of X^N − 1; the repository's gf2_fast RIS backend (make fast) for all distance searches; verify/validate_candidate.py as the only gate. Compute: one Apple M2 Pro (12 cores), ~11 hours wall-clock including verification. The search code is not part of this PR; the method above and the reproduction below are self-contained.

Reproduction

import sys; sys.path.insert(0, "research/kit")
from group_algebra import build_2bga, cyclic_product
mul, _ = cyclic_product(315)                      # Z_315, element index = exponent
HX, HZ = build_2bga(mul, [0, 1, 8], [0, 52, 229])  # f = 1 + x + x^8, g = 1 + x^52 + x^229

This reproduces the submitted checks check-for-check with the same qubit labelling (qubit e < 315 is the left-block element x^e, qubit 315 + e the right block). k = 2·deg gcd(f, g, x^315 − 1) = 12.

Parity checks

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