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[[504,18,40]] d ≤
n
504
k
18
d
40
kd²/n
57.143
w
8
X/Z
1.45

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Distance

X/Z asymmetry 1.45 · d_X ≤ 40, d_Z ≤ 58 · w_X = 8, w_Z = 8 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 40 · witness weight 40 (claimed upper_bound)
witness operator (support, 40 qubits)
[3, 30, 42, 59, 62, 72, 84, 88, 105, 131, 143, 145, 161, 169, 195, 203, 221, 226, 229, 230, 242, 259, 263, 272, 295, 297, 304, 328, 333, 356, 357, 371, 392, 393, 401, 430, 460, 477, 490, 494]
d_Z 58 · witness weight 58 (claimed upper_bound)
witness operator (support, 58 qubits)
[5, 7, 26, 28, 30, 34, 36, 37, 45, 47, 52, 65, 68, 86, 90, 94, 97, 98, 103, 106, 107, 112, 115, 119, 121, 124, 137, 158, 179, 187, 188, 191, 208, 210, 230, 236, 239, 248, 251, 276, 288, 296, 308, 334, 350, 358, 384, 388, 389, 397, 398, 423, 424, 438, 457, 461, 473, 478]
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 8 · H_Z 8
qubit degrees H_X 4 · H_Z 4
trapping sets H_X (1,4)×504 (2,6)×7056 (3,6)×2520 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,4): 504 (2,6): 7056 (3,6): 2520 (3,8): 140616 (3,10): 14112
trapping sets H_Z (1,4)×504 (2,6)×7056 (3,6)×2520 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,4): 504 (2,6): 7056 (3,6): 2520 (3,8): 140616 (3,10): 14112

Construction & provenance

authors @FarLab
provenance submitted through the challenge
novelty novelty not audited
construction Cyclic (single-circulant-pair) generalized-bicycle code over Z_252 (research/kit/gf2poly.py cyclic_gb): a(x) = 1 + x154 + x163 + x192, b(x) = 1 + x153 + x167 + x179; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with circ(v)[i, (i + j) mod 252] = v[j]. n = 2m = 504, k = 2 deg gcd(a, b, x252 - 1) = 18, check weight 8 = 4+4. gcd(a, b, x252 - 1) has degree 9 (as a little-endian bit integer: 863); a and b were enumerated as weight-4/4 multiples of that divisor via residue tables x^i mod g.
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

[[504,18,40]] — weight-8 cyclic generalized-bicycle code over Z_252 (designed divisor, supports of weight 4 and 4)

Direction & hypothesis

Cell: unrestricted x weight-8 (check weight 8), n band 401 to 600, where the w <= 8 frontier at k between 16 and 40 is set by generalized-bicycle codes at n 336 to 378 ([[336,28,20]], [[336,24,24]], [[378,32,19]], [[378,18,27]]) and a few entries inside the band. The hypothesis: with k designed through the divisor structure of x^m - 1 (or through the group algebra of a non-abelian group) and low-weight multiples enumerated exactly rather than sampled, n 400 to 600 gives k 18 to 30 at distances above what the n ~ 340 to 380 entries reach. At (n, k) = (504, 18) the smallest distance not dominated by a board entry with n' <= n, k' >= k, w' <= 8 was 33 when this was gated; the target was a strict Pareto advance by a margin, not a tie.

What was searched

  • Family: cyclic generalized-bicycle codes H_X = [circ(a) | circ(b)] over Z_m with k = 2 deg gcd(a, b, x^m - 1) designed through a divisor, for every m in [201, 300] (n = 2m in [402, 600]), odd and even m alike (for even m, x^m - 1 = (x^(m/2) - 1)^2 and the prime-power factors carry multiplicities).
  • Two exact enumerators replace Prange sampling. Weight-3 words: for every prime-power divisor q of x^m - 1 the residues x^i mod q are tabulated and every trinomial 1 + x^i + x^j with q | a is read off (r[j] = r[i] + 1), which gives deg gcd(a, b, x^m - 1) for every trinomial pair exactly, so all weight-(3,3) pairs with k in band are seen for every m. Weight-4 words: divisors g with degree in [8, 36] are sampled (up to 100 to 150 per m, excluding multiples of x^m' + 1 for proper m' | m, whose multiples factor as (1 + x^m')(...) and have tiny distance) and every weight-3 and weight-4 multiple of g containing x^0 is listed from the residue table mod g; up to 150 to 300 random pairs per divisor give the (3,4) and (4,4) candidates.
  • Pairs are deduplicated under rotation, the multiplier automorphisms x -> x^u, swap and reciprocal; pairs whose offsets share a factor with m (direct sums) are dropped before any trial is spent.
  • Funnel: 122,376 distinct pairs screened at 600 gf2_fast RIS trials (1 thread each, 24 to 56 worker processes); a pair is promoted only while its reading still clears the board's frontier threshold for its (n, k, w) (the smallest d no entry with n' <= n, k' >= k, w' <= w reaches): 11,500 reached 20,000 trials, 549 reached 200,000 trials, 474 survived; survivors were then re-measured at 1,000,000 and 20,000,000 fresh-seed trials (26 to 60 threads) and the best per (n, k, w) cell staged, gated and laddered.

Evidence trail

Distances are witness-backed upper bounds. Every operator in the table was validated in Python (research/kit/surrogate.validate_logical: commutes with the opposite checks, outside its own row space, weight recounted) before it was recorded; the lightest one is the witness in the code file.

| instrument | side | trials per side | lightest logical | |---|---|---:|---:| | sweep stage 3, gf2_fast RIS (pair depth 8) | both | 200,000 | 52 | | re-measure, gf2_fast RIS, fresh seed | both | 1,000,000 | 42 | | descent pass, gf2_fast RIS, seed 718539468 | both | 20,000,000 | 40 | | deep ladder rung 0, fast seed 51808 | X found | 20,000,000 | 40 | | deep ladder rung 1, fast seed 59727 | X found | 20,000,000 | 42 | | deep ladder rung 2, fast seed 67646 | X found | 20,000,000 | 42 |

Board gate (verify/validate_candidate.py through research/kit/coordination.py gate_and_record): passed = True, board_advancing = True, labels ['advances the weight-8 x unrestricted board', 'literature novelty UNVERIFIED'].

Claim: witness-backed upper bound d <= 40 (X <= 68, Z <= 40), not exact. The ladder's three fresh seeds at 20,000,000 trials per side came back at 40, 42, 42: none found a logical lighter than 40; verdict corroborated. Literature novelty unverified; board-relative novelty is the gate's (verify/validate_candidate.py) verdict above.

Dead ends

  • Screening inflation at n >= 500. The 200,000-trial readings of the sweep survivors are far from converged at

    • these lengths: a [[584,22]] weight-8 cyclic pair read 85 at 600 trials and 30 at 20,000; a [[504,18]] pair read 52 at 200,000, 42 at 1,000,000 and 2,000,000, and 40 at 20,000,000; a [[600,14]] metacyclic 2BGA read 62 at 2,000,000 and the gate's own pass found 50. Every survivor was therefore re-measured at 1,000,000 and then 20,000,000 fresh-seed trials before it was staged, and only the 20,000,000-trial reading was claimed.

  • Degenerate divisors (cyclic sweep). A divisor g that is a multiple of x^m' + 1 for a proper m' | m has many

    • weight-4 multiples of the form (1 + x^m')(1 + x^i), and every such pair had d <= 7 at 600 trials (k = 102 to 136 at d 2 to 4 on Z_204, k = 134 at d <= 3 on Z_201); these divisors were excluded from the sweep.

  • Weight-(3,3) cyclic pairs. Enumerated exhaustively for every m in [201, 300]: the connected pairs with k 14 to 16

    • read d 22 to 26 at 200,000 trials, tying or trailing [[420,14,22]], [[434,16,22]], [[508,14,24]] and [[510,16,26]]; no cyclic weight-6 pair with k >= 18 cleared its threshold, so the cyclic family does not reach the empty k 20 to 60 region of the weight-6 cell.

  • Random 2BGA on metacyclic groups of order 201 to 300: k = 0 in 49 percent of 400,000 draws (3+3, 3+4, 4+4

    • supports) and k >= 14 in about 2 percent. Weight-6 draws with k = 24 to 32 at n = 504 to 560 (C_p x|_r C_q of order 252 to 280) read only d 12 at 200,000 trials, one above the threshold, and were not pursued; the weight-8 metacyclic survivors read 39 to 74 at 200,000 trials, readings the deeper passes cut sharply wherever they were re-measured (first item).

Tools

Model: Claude Fable 5.1 (Claude Code), matching provenance.model; one agent of a ten-agent frontier campaign, running on a Brev n2d-highcpu-64 box with gf2_fast (verify/) at 24 to 60 threads. Kit modules: research/kit/gf2poly.py (cyclic_gb, factor_squarefree, designed_k), research/kit/group_algebra.py (metacyclic, build_2bga), research/kit/surrogate.py (distance_rand_witness, pair depth 8), research/kit/prescreen.py (block_structure), research/kit/submit.py (make_submission, save_submission), research/kit/coordination.py (gate_and_record over verify/validate_candidate.py). The sweep driver was a session script implementing the residue-table enumeration described above (method stated in full in "What was searched" so it can be rewritten). Compute: about 45 CPU-core hours for the cyclic sweep (24 to 56 worker processes for 75 minutes) plus about 5 CPU-core hours of re-measurement, gate and ladder (32 threads, 60 minutes).

Reproduction

Construction (also in provenance.construction): Cyclic (single-circulant-pair) generalized-bicycle code over Z_252 (research/kit/gf2poly.py cyclic_gb): a(x) = 1 + x^154 + x^163 + x^192, b(x) = 1 + x^153 + x^167 + x^179; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with circ(v)[i, (i + j) mod 252] = v[j]. n = 2m = 504, k = 2 deg gcd(a, b, x^252 - 1) = 18, check weight 8 = 4+4. gcd(a, b, x^252 - 1) has degree 9 (as a little-endian bit integer: 863); a and b were enumerated as weight-4/4 multiples of that divisor via residue tables x^i mod g.

import sys; sys.path[:0] = ['research/kit', 'verify']
from gf2poly import cyclic_gb, designed_k
HX, HZ = cyclic_gb(252, [0, 154, 163, 192], [0, 153, 167, 179])
assert designed_k(252, [0, 154, 163, 192], [0, 153, 167, 179]) == 18

Ladder seeds: 51808, 59727, 67646 (gf2_fast, pair depth 8, 20,000,000 trials per side each).

Parity checks

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