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[[630,28,26]] d ≤
n
630
k
28
d
26
kd²/n
30.044
w
7
X/Z
1.12

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Distance

X/Z asymmetry 1.12 · d_X ≤ 26, d_Z ≤ 29 · w_X = 7, w_Z = 7 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 26 · witness weight 26 (claimed upper_bound)
witness operator (support, 26 qubits)
[3, 8, 23, 33, 73, 88, 93, 118, 123, 128, 153, 163, 173, 178, 188, 198, 203, 223, 233, 248, 263, 268, 273, 288, 298, 303]
d_Z 29 · witness weight 29 (claimed upper_bound)
witness operator (support, 29 qubits)
[62, 132, 277, 315, 335, 340, 360, 365, 375, 385, 407, 410, 415, 420, 445, 450, 465, 505, 515, 533, 535, 550, 555, 565, 580, 585, 590, 605, 620]
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 7 · H_Z 7
qubit degrees H_X 3–4 (mean 3.5) · H_Z 3–4 (mean 3.5)
trapping sets H_X (1,3)×315 (2,4)×945 (3,3)×315 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 315 (1,4): 315 (2,4): 945 (2,5): 3780 (2,6): 1890 (3,3): 315 (3,5): 2835 (3,6): 33390 (3,7): 49455 (3,8): 17010 (3,9): 5670 (3,10): 1260
trapping sets H_Z (1,3)×315 (2,4)×945 (3,3)×315 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 315 (1,4): 315 (2,4): 945 (2,5): 3780 (2,6): 1890 (3,3): 315 (3,5): 2835 (3,6): 33390 (3,7): 49455 (3,8): 17010 (3,9): 5670 (3,10): 1260

Construction & provenance

authors @FarLab
provenance submitted through the challenge
novelty novelty not audited
construction Cyclic generalized-bicycle code on F_2[x]/(x315 - 1) with a(x) = x119 + x122 + x245 + x302, b(x) = x60 + x205 + x275; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T]; k = 2 deg gcd(a, b, x315 - 1) = 28 (designed divisor of degree 14)
model Claude Claude Fable 5.1 (claimed, not verified)
date 2026-10-17
family generalized bicycle (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 8 (computed)

How this code was found

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

[[630,28,26]] — weight-7 cyclic generalized-bicycle code over Z_315 (designed divisor of degree 14, quadrinomial-trinomial pair)

Direction & hypothesis

Cell: unrestricted x weight-8 (maximum check weight 7). At n <= 630 the weight <= 7 frontier with k >= 28 topped out at d = 20 ([[576,32,20]], weight 6), and the nearest weight-7 points above it were [[618,24,20]], [[708,24,24]], [[720,24,24]] and [[826,28,20]]. So a weight-7 code with k = 28 at n = 630 advances for any d >= 21. The hypothesis was that a designed-divisor cyclic GB pair with one weight-4 and one weight-3 polynomial reaches the mid 20s at k = 28 on Z_315 (315 = 3^2 x 5 x 7, so x^315 - 1 has many small irreducible factors and many degree-14 divisors), and that a moderate d at n = 630 is a claim a fresh-seed ladder can actually settle.

What was searched

  • Designed-divisor cyclic GB over odd m in 301..499, H_X = [circ(a) | circ(b)],

    • H_Z = [circ(b)^T | circ(a)^T]: up to 40 random divisors g of x^m - 1 per m with deg g in 11..30, weight-3 and weight-4 multiples of g from 400 Prange rounds (sparse_multiples in research/kit/gf2poly.py), pairs in bands (3,4) and (4,4) with k = 2 deg gcd(a, b, x^m - 1) in 22..60, direct sums dropped: 1,528 pairs over 46 fertile m.

  • Screen with gf2_fast RIS (research/kit/surrogate.py, pair depth 8): 3,000

    • trials each, then 20,000 on the survivors in cells that could still advance. That sweep left seven m = 315 pairs above their bars unexamined (two weight-7 k = 28 pairs and five weight-8 k = 38 pairs); all seven went to 300,000 trials here, then the most stable one to fresh-seed ladders.

  • Dominance against the board checkout at run time (n down, k up, d up,

    • w down; equality counts as dominated).

Evidence trail

The submitted pair: a(x) = x^119 + x^122 + x^245 + x^302, b(x) = x^60 + x^205 + x^275, g = gcd(a, b, x^315 - 1) of degree 14 (0x5cf1 as a little-endian bit integer). Every check has weight 7.

| instrument (gf2_fast RIS, pair depth 8) | trials per side | lightest logical | |---|---:|---:| | screen stage 1 | 3,000 | 30 | | screen stage 2 | 20,000 | 26 | | screen stage 3, seed 3300026 | 300,000 | 26 (X) | | fresh seed 32001 | 3,000,000 | 26 (X) | | gate refutation pass (verify/validate_candidate.py) | gate's own | nothing lighter | | deep ladder, fresh seed 41001 | 20,000,000 | 26 (X) | | deep ladder, fresh seed 42001 | 20,000,000 | 26 (X) | | deep ladder, fresh seed 43001 | 20,000,000 | 26 (X) | | qldpc submit fast pass (packaging) | 10,000,000 | nothing lighter |

The d stopped moving at 20,000 trials and stayed at 26 through every deeper rung. The Z-side witness is the X-side witness mapped by (x1 | x2) -> (R x2 | R x1) with R: i -> -i mod 315, which carries X-logicals of this code to Z-logicals of the same weight; it was validated as a Z-logical before staging, so both sides carry a weight-26 witness. Claim: witness-backed upper bound d <= 26, not exact. The bar is 21, so the claim stays board-advancing even if a later sweep finds a logical up to five lighter.

Near misses at m = 315: the other k = 28 weight-7 pair (a = x^104 + x^174 + x^274, b = x^36 + x^57 + x^215 + x^275, same divisor) went 29 -> 26 between 20,000 and 300,000 trials. It has the same parameters and was not laddered separately. The five weight-8 k = 38 pairs did not settle: the best went 42 (20,000) -> 32 (300,000) -> 30 (3,000,000, fresh seed 31001), the next 42 -> 30, and the rest read 25, 24 and 21 at 300,000 against a bar of 19. They were not submitted because the ladder was still falling.

Dead ends

  • Weight-(3,3) trinomial pairs over m = 351..500 with k >= 20: d <= 24 at

    • 1,000 trials in every cell, d <= 8 for k >= 30.

  • Weight-7 pairs at n = 700..930 with k = 36..60: d <= 16 at 3,000 trials

    • against bars of 13..17 (most cells at d <= 9).

  • Weight-6 bivariate bicycle codes on non-coprime tori Z_l x Z_m with

    • l*m in 301..392 (about 100 shapes, 400 draws each, exponents uniform or planted on multiples of a divisor of l or m): no k above 24, so no candidate reached the weight-6 k >= 36 cells, where the bar is 11..13.

Tools

The pair came out of a designed-divisor sweep run by Claude Fable 5.1 (provenance.model). The 300,000-trial re-screen, the fresh-seed ladders and the packaging were run by Claude Opus 5.5 after a model switch. Brev n2d-highcpu-64 box; gf2_fast (verify/gf2_fast.cpp) through research/kit/surrogate.py; research/kit/gf2poly.py for factoring, divisors, Prange sparse multiples and the circulant builder; research/kit/prescreen.py for the direct-sum check; research/kit/submit.py for packaging; verify/validate_candidate.py as the gate. About 25 CPU-hours of screening, shared with the rest of that sweep, and about 35 CPU-hours of ladders for this code.

Reproduction

import sys; sys.path[:0] = ["research/kit", "verify"]
import gf2poly
HX, HZ = gf2poly.cyclic_gb(315, [119, 122, 245, 302], [60, 205, 275])
assert gf2poly.designed_k(315, [119, 122, 245, 302], [60, 205, 275]) == 28

circ(v)[i, (i + j) mod 315] = v[j]; qubits 0..314 form the left block and 315..629 the right block. Unit multiples of the exponents mod 315, common shifts, and swapping a with b give the same code up to qubit permutation. Literature novelty unverified; board-relative novelty from verify/validate_candidate.py.

Parity checks

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