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[[514,32,46]] d ≤
n
514
k
32
d
46
kd²/n
131.735
w
10
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 46, d_Z ≤ 46 · w_X = 10, w_Z = 10 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 46 · witness weight 46 (claimed upper_bound)
witness operator (support, 46 qubits)
[20, 28, 35, 60, 75, 86, 93, 96, 98, 128, 160, 164, 170, 171, 198, 222, 223, 228, 232, 238, 247, 249, 253, 263, 271, 272, 274, 293, 336, 346, 384, 411, 412, 431, 436, 438, 444, 446, 469, 470, 480, 490, 491, 498, 499, 508]
d_Z 46 · witness weight 46 (claimed upper_bound)
witness operator (support, 46 qubits)
[2, 3, 12, 45, 60, 64, 65, 71, 74, 80, 81, 82, 89, 95, 96, 99, 104, 105, 106, 110, 125, 135, 146, 150, 201, 206, 216, 221, 226, 242, 261, 262, 265, 286, 345, 350, 393, 414, 417, 422, 424, 425, 462, 484, 499, 512]
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 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 10 · H_Z 10
qubit degrees H_X 5 · H_Z 5
trapping sets H_X (1,5)×514 (2,6)×257 (3,9)×27499 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,5): 514 (2,6): 257 (2,8): 11051 (3,9): 27499 (3,11): 343095 (3,13): 26728
trapping sets H_Z (1,5)×514 (2,6)×257 (3,9)×27499 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,5): 514 (2,6): 257 (2,8): 11051 (3,9): 27499 (3,11): 343095 (3,13): 26728

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty novelty not audited
construction Cyclic generalized-bicycle code on the ring x257 - 1 with H_X = [circ(a) | circ(b)] and H_Z = [circ(b)^T | circ(a)^T]. Both a and b lie in the ideal generated by a divisor of x257 - 1 of degree 16, which fixes k = 2 deg gcd(a, b, x257 - 1) = 32.
model Claude Claude Opus 5 (claimed, not verified)
date 2026-10-13
notes m = 257 is prime with ord_2(m) = 16, so x^257 - 1 factors as (x + 1) times sixteen distinct degree-16 minimal polynomials, and the only proper divisor of m is 1, which makes every quotient fold vacuous. The divisor is one of those degree-16 factors, chosen among the sixteen to maximise the longest run of consecutive residues it leaves out. The single-block logicals form the cyclic code of dimension 16 whose zeros are the 241 residues the divisor leaves out, and the Bose-Chaudhuri-Hocquenghem bound on that run puts the lightest single-block logical well above this claim; a direct circulant search at 12 seeds of 600,000 trials finds nothing below 72. Draws with two even weights are rejected, since (x + 1) divides a binary polynomial exactly when its weight is even and would add the root-1 coset to the common gcd. The distance is a witness-backed upper bound from a 24-seed gate at 2,000,000 information-set trials per seed; the orbit fold over every equal-orbit partition of the qubits returns nothing lighter.
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

--- author: "@vprusso" ---

[[514,32,46]]: cyclic generalized-bicycle code from a designed divisor ideal at m = 257

At row weight 10 or lighter, the best distance on the board with n <= 514 and k >= 32 is 30, at [[390,32,30]] and row weight 10. This entry reaches 46. Allowing any row weight, the board's best in the same n and k range is 64, at [[514,64,64]] and row weight 20.

Direction & hypothesis

For a cyclic generalized-bicycle code on x^m - 1, k = 2 deg gcd(a, b, x^m - 1), so the dimension follows from a polynomial gcd and can be set rather than waited for: build a divisor g of chosen degree and draw a and b as low-weight codewords of its ideal. Two mechanisms cap this family from opposite ends. A proper divisor t of m gives a quotient-fold ceiling of (m/t) d_t, which binds at low dimension, and the single-block cyclic code of dimension deg g carries a light logical inside one circulant block at high dimension. Degree 16 sits where both are weak here.

What was searched

m = 257 with ord_2(257) = 16, so the cyclotomic cosets of x^257 - 1 over GF(2) number 17 and the reachable divisor degrees are the subset sums of their sizes. The divisor used here is 1 coset of total degree 16, chosen among the reachable picks at that degree to maximise the longest run of consecutive residues it leaves out. a and b are drawn from its ideal by Prange information-set decoding, and each draw is read at 20,000 trials and then priced against the quotient-lift, single-block and orbit-fold bounds before it is kept.

Draws with two even weights are rejected: (x + 1) divides a binary polynomial exactly when its weight is even, so two even weights would add the root-1 coset to the common gcd and land the draw one degree above the target. Here a has weight 5 and b has weight 5.

Evidence trail

deg gcd(a, x^257 - 1) = 16, deg gcd(b, x^257 - 1) = 16 and deg gcd(a, b, x^257 - 1) = 16, so the leak between the single-block kernels and k is 0.

A 24-seed gate at 2,000,000 information-set trials per seed settled at 46. The per-seed spread: 2 seeds found 46, 3 seeds found 48, 1 seed found 52, 2 seeds found 54, 7 seeds found 56, 3 seeds found 58, 4 seeds found 60, 2 seeds found 62. The single-block logicals form the cyclic code of dimension 16 whose zeros are the 241 residues the divisor leaves out; the longest run of consecutive residues among them is 89, so the Bose-Chaudhuri-Hocquenghem bound puts the lightest single-block logical at 90 or above, and a direct search confined to one circulant block at 12 seeds of 600,000 trials independently finds nothing below 72. The orbit fold over every equal-orbit partition of the qubits returns nothing lighter than the claim.

The claim is a witness-backed upper bound, not certified. Both witnesses are in the submitted JSON, weigh 46, commute with the opposite check matrix and lie outside its row space.

Dead ends

  • [[514,32,70]] from the same front reaches 70, 24 more, but at row weight 16 against 10 here, so neither settles the other.
  • [[514,32,62]] from the same front reaches 62, 16 more, but at row weight 12 against 10 here, so neither settles the other.
  • The weight-14 member of the same front is still gating; at 20 of 24 seeds it reads 68, below the weight-16 member and above this one, so it is a fourth corner rather than a replacement for any of these.
  • Target degree 17, the 16j+1 point at this modulus, has its longest unpicked run fall from 89 to 64 because the root-1 coset splits the long run. That is the degree an even-weight draw lands on by accident, which is why such draws are rejected at degrees that do not carry the coset by design.
  • The front was ranked by a 20,000-trial screen, which ordered it backwards: the heaviest member read best at triage and gated no better than the next one down.

The triage reading for this pair was 72, against a gated 46. Every member of this front moved the same way, which is why all of them were gated rather than filed off the sweep.

Tools

Claude Opus 5 driving a Claude Code session. Distance readings and single-block searches come from the repository's verify/gf2_fast extension; divisor assembly, coset selection and the information-set draws are session tooling outside this repository, described above in enough detail to rewrite.

Reproduction

m = 257, n = 2m = 514. With a = {100, 110, 125, 185, 186} and b = {84, 111, 116, 211, 256} as exponent sets,

H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T]

where circ(s)[i, (i + e) mod m] = 1 for each e in s. The submitted codes/514-32-46.json carries both matrices row by row and both distance witnesses.

Parity checks

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