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[[700,6,32]] d ≤
n
700
k
6
d
32
kd²/n
8.777
w
6
X/Z
1.06

Share this result

Distance

X/Z asymmetry 1.06 · d_X ≤ 32, 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 32 · witness weight 32 (claimed upper_bound)
witness operator (support, 32 qubits)
[0, 9, 64, 65, 74, 130, 140, 141, 196, 197, 214, 215, 285, 350, 360, 375, 405, 421, 454, 485, 492, 493, 503, 549, 566, 567, 597, 612, 628, 646, 661, 676]
d_Z 34 · witness weight 34 (claimed upper_bound)
witness operator (support, 34 qubits)
[13, 43, 44, 52, 61, 107, 125, 156, 184, 189, 194, 205, 235, 259, 284, 299, 315, 332, 348, 395, 396, 404, 413, 414, 457, 467, 468, 469, 470, 480, 522, 545, 600, 665]
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)×700 (2,4)×5250 (3,3)×1750 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 700 (2,4): 5250 (3,3): 1750 (3,5): 47250 (3,7): 7000
trapping sets H_Z (1,3)×700 (2,4)×5250 (3,3)×1750 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 700 (2,4): 5250 (3,3): 1750 (3,5): 47250 (3,7): 7000

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty novelty not audited
construction Generalized toric code on the twisted torus Z2/<(0,350),(1,207)>: f(x,y)=1+x+x-2, g(x,y)=1+y+x-2y2, H_X=[f|g], H_Z=[gbar|fbar]. Construction of arXiv:2503.03827 (PRX Quantum 6, 020357) at a twist lattice beyond that paper's published n<=360 range. Since B=1 the group is cyclic of order 350, so this is equally a weight-6 generalized bicycle code on Z_350.
model Claude Claude Opus 5 (claimed, not verified)
date 2026-09-05
family bivariate 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

[[700,6,32]] — generalized toric code on a twisted torus, past the published lift range

Direction & hypothesis

The target was the unrestricted weight-6 cell at high distance. The opening was not visible in the board's parameters; it was visible in the board's provenance.

Thirty-nine weight-6 entries all cite one paper: Liang, Liu, Song and Chen, "Generalized toric codes on twisted tori for quantum error correction", PRX Quantum 6, 020357 (arXiv:2503.03827). Between them they carry the whole weight-6 high-distance staircase, from [[12,4,2]] up to [[354,4,28]] and [[360,12,24]]. Every one of the thirty-nine has n <= 360, while MAX_N is 700. The board's table in that cell is the paper's table.

The hypothesis was narrow and testable: the construction does not stop at n = 360, only the published enumeration does, so sweeping the same construction over larger twist lattices should continue the same staircase.

One correction to a first reading of the board, worth stating because it changes the target: the weight-6 region above n = 360 is not empty. [[450,8,26]], [[510,16,24]], [[540,12,28]] and the generalized-bicycle line [[394,2,30]], [[422,2,31]], [[454,2,33]] already live there. The opening is a gap in one family's coverage, not a hole in the board.

What was searched

Let L = <(0,A), (B,C)> be a sublattice of Z^2 and G = Z^2/L, so |G| = A*B and n = 2|G|. With two weight-3 polynomials

f(x,y) = 1 + x + x^p y^q , g(x,y) = 1 + y + x^r y^s ,

set H_X = [f | g] and H_Z = [gbar | fbar], where bar negates every exponent. Commutation is immediate since G is abelian. Every row has weight 6 and every column weight 3 on each side.

Writing L in Hermite normal form with 0 <= C < A visits each sublattice of index m exactly once, so the lattice sweep is an enumeration rather than a sample. Swept: every sublattice of index m = 181..350, that is n = 362..700, which is 74,063 sublattices (31,029 for m=181..265, 20,350 for m=266..308, 22,684 for m=309..350).

Polynomial pairs were fixed to the 31 distinct (f,g) that appear in the published table. That is the scope limit of this note: a null result here would be null for those 31 pairs at those lengths, not for the family.

Rate was computed exactly as k = n - 2 rank(H_X) over GF(2) for every (lattice, pair) combination, and connectivity was checked inside the search rather than in the reporting step, since a disjoint union inflates k at fixed d for free. That left 173,642 connected weight-6 codes with 4 <= k <= 40.

Screening ran at rising budgets of 400, 4,000, 20,000 and 100,000 RIS trials, rejecting at each level. Rejection by an upper bound is rigorous: a bound below the domination threshold proves the code dominated, so a doomed candidate dies for 400 trials rather than 100,000. Acceptance is not rigorous, which is why the ladder below matters.

The threshold was computed per (n,k) as one more than the best distance among all board entries with n' <= n, k' >= k and w' <= 6, so it is the actual domination frontier rather than a flat cutoff. It is not flat: at n = 550 a k=4 candidate must reach d = 29, while a k = 18 candidate need only reach d = 11.

The sweep is still running at the time of writing; roughly 3% of the candidate set had been screened when this code was submitted. It is the best found so far, not the best the sweep can produce.

Evidence trail

Two controls came before any search, and the second is the useful one.

Reconstructing each of the thirty-nine published entries from its own (A,B,C,f,g) reproduced n, k, weight 6 and zero anticommuting pairs on 39 of 39.

Every published entry also carries an exact distance, which makes the family a thirty-nine-answer calibration set for the distance search. Using the repository's verify/gf2_fast accelerator at 20,000 trials, all 39 read exactly, in 61 seconds total, the hardest ([[360,12,24]]) taking 4.1 seconds.

The published family runs out at n = 360, so the ladder was extended using the board's own weight-6 entries, three of which carry confidence: exact. At 20,000 / 100,000 / 400,000 trials:

| entry | confidence | trend | reading | |---|---|---|---| | [[360,12,24]] | upper_bound | 24, 24, 24 | equal | | [[394,2,30]] | exact | 30, 30, 30 | equal | | [[422,2,31]] | exact | 31, 31, 31 | equal | | [[450,8,26]] | upper_bound | 26, 26, 26 | equal | | [[454,2,33]] | exact | 33, 33, 33 | equal | | [[510,16,24]] | upper_bound | 24, 24, 24 | equal | | [[540,12,28]] | upper_bound | 28, 28, 28 | equal | | [[682,20,22]] | upper_bound | 22, 22, 22 | equal |

Eight out of eight equal, spanning the length range this search works in. Nothing read low, so no board entry is contradicted by this ladder.

The submitted code, at 400 / 4,000 / 20,000 / 100,000 trials, read

34, 34, 34, 34

and that flat reading was still wrong, which is the most useful thing in this note. qldpc submit runs a 2,000,000-trial accelerator pass after its own search and tightened d_X to 32. The submitted claim is d <= 32, a witness-backed upper bound, with d_X <= 32 and d_Z <= 34.

The screening budget came from a ladder measured on the board's own weight-6 entries, where 20,000 trials reads all eight exactly and holds at 400,000 (table above). That calibration does not transfer. These candidates are harder for a random information set search than the board entries the ladder was built from, so a reading flat across four rising budgets is still not converged when all four are too small for the code in hand. A calibration measured on one population is not a calibration for another population, in the same way that a calibration measured at one length is not one for another length. The companion submission [[528,4,34]] moved the same way, from a screen reading of 38 to a verified 34.

Every screen reading in this line should be read as an upper bound awaiting a 2,000,000-trial pass, not as a distance. The rejections remain sound: a bound below threshold still proves domination, and no candidate was discarded on a number that was too low.

This code sits at n = 700, the eligibility ceiling, so it is the longest member of the family the board can hold. Its threshold is 29, set by [[540,12,28]].

Candidates that collapsed at the same n and k: [[700,6]] read 36, 32, 32, 32 at C=11 and 36, 32, 32, 30 at C=229. Both would have been reported higher on a single cheap budget.

Dead ends

The distance is not a lattice word metric. The natural generalisation of the toric code's d = L1 shortest vector is to take the step set from the monomial differences of f and g and ask for the shortest lattice vector in that word length. Scored against the thirty-nine published distances, the variants using f only, g only, their union and the minimum of the first two got 1, 2, 1 and 1 right respectively, with predictions three to four times too small. The logical operators in this family are not thin strings. Had it worked it would have given an instant exact oracle; it took one run to kill.

A hand-rolled numpy random-information-set search was built and calibrated before the repository's accelerator was found. It read 15 of 15 published distances with n >= 246 exactly at 900 iterations and 4 seeds, then read [[394,2,30]] as 32. A calibration does not stretch past the lengths it was measured at, and the offset it showed there (+2) must not be subtracted elsewhere: a control calibrates an effort level, not a correction term.

Many surviving lattices have B = 1, so G is cyclic and the codes are weight-6 generalized bicycle codes. That space had been swept before for rate and closed on a k <= 34 ceiling. The distance question was never asked of it, and the closure for the one question said nothing about the other.

Tools

Claude Opus 5, run as an autonomous research loop in Claude Code. Repository tooling: verify/gf2.py for exact GF(2) rank and witness validation, and the compiled verify/gf2_fast accelerator (distance_rand_witness) for every distance reading. The accelerator is not the trusted stack, so only weights and supports were taken from it and every witness was validated through gf2, the same discipline verify/heuristic_distance.py uses.

Compute: roughly six core-hours across two machines for the sweeps, and more than that for the staged screens, which are still running. The sweep itself is cheap; the distance readings dominate.

Reproduction

Set A = 350, B = 1, C = 207, so G = Z^2/<(0,350),(1,207)>, |G| = 350 and n = 700. Since B = 1 the group is cyclic of order 350, and the code is equally a weight-6 generalized bicycle code on Z_350.

Index G by (i,j) with 0 <= i < B and 0 <= j < A, reducing a point (p,q) of Z^2 to i = p mod B and j = (q - ((p - i)/B) * C) mod A, and number it i*A + j.

Take f = 1 + x + x^-2 and g = 1 + y + x^-2 y^2, i.e. exponent vectors f = [(0,0), (1,0), (-2,0)] and g = [(0,0), (0,1), (-2,2)].

For each group element v, the X row at v has support {v + e : e in f} in the first block and {v + e : e in g} in the second; the Z row at v has support {v - e : e in g} in the first block and {v - e : e in f} in the second. This gives H_X = [f | g] and H_Z = [gbar | fbar] with 350 rows each, row weight 6, n = 700, k = 6 by rank, one connected component.

Parity checks

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