[[630,26,35]] · QEC Challenge

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[[630,26,35]] d ≤

630

kd²/n

50.556

X/Z

2.63

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Distance

X/Z asymmetry 2.63 · d_X ≤ 92, d_Z ≤ 35 · 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 92 · witness weight 92 (claimed upper_bound)

witness found by @FarLab · research/kit/surrogate.lightest_logical · found at 300 trials · survived 300 trials · 2026-10-17

witness operator (support, 92 qubits)

[5, 6, 7, 25, 28, 33, 36, 56, 68, 72, 80, 90, 91, 94, 98, 109, 123, 127, 129, 137, 160, 167, 169, 170, 176, 186, 188, 189, 198, 209, 211, 216, 241, 242, 244, 251, 256, 258, 262, 266, 271, 273, 275, 284, 285, 298, 312, 323, 325, 338, 357, 365, 377, 380, 381, 397, 398, 399, 404, 405, 408, 410, 411, 414, 428, 437, 443, 447, 456, 459, 473, 483, 485, 490, 495, 506, 520, 524, 525, 527, 536, 554, 563, 570, 581, 582, 583, 586, 606, 609, 615, 623]

d_Z 35 · witness weight 35 (claimed upper_bound)

witness found by @FarLab · research/kit/surrogate.distance_rand_witness (gf2_fast) · found at 2×10⁷ trials · survived 2×10⁷ trials · 2026-10-17

witness operator (support, 35 qubits)

[5, 7, 24, 28, 45, 62, 108, 113, 119, 125, 131, 184, 201, 205, 210, 213, 222, 251, 257, 291, 296, 308, 364, 382, 416, 445, 447, 486, 496, 509, 520, 527, 549, 551, 566]

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)×630 (2,6)×8820 (3,6)×2835 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_X

(1,4): 630 (2,6): 8820 (3,6): 2835 (3,8): 176715 (3,10): 17640

trapping sets H_Z (1,4)×630 (2,6)×8820 (3,6)×2835 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_Z

(1,4): 630 (2,6): 8820 (3,6): 2835 (3,8): 176715 (3,10): 17640

Construction & provenance

authors @FarLab

provenance submitted through the challenge

novelty novelty not audited

construction Cyclic generalized-bicycle code over Z_315: H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with a = 1 + x¹²⁶ + x¹³⁸ + x¹⁴³ and b = x¹⁶⁴ + x¹⁸⁸ + x²⁰⁶ + x²⁶⁸; gcd(a, b, x³¹⁵ - 1) has degree 13 (x + 1 times an irreducible factor of degree 12), so k = 26 by design. Every check has weight 8.

model 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

[[630,26,35]] — weight-8 cyclic GB code over Z_315 (designed divisor, degree 13)

Direction & hypothesis

Cell: unrestricted x weight-8. At n = 630 the weight-8 column is held by [[630,34,32]] (designed-divisor two-block code on Z_315, w = 4 + 4); a code with k in 26..34 at n <= 630 needs d >= 33 to advance it. The hypothesis was that a divisor of degree 11..14 (k = 22..28) leaves enough weight-4 words in its ideal for pairs whose distance clears the k = 32..34 entries, and 315 = 3^2 x 5 x 7 gives x^315 - 1 many small irreducible factors to build divisors from.

What was searched

Designed-divisor cyclic GB codes over odd m in 301..499: 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 weight 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; at m = 315 the (4,4) band gave 10 pairs with k = 26, 8 with k = 30, 6 with k = 32 and 5 with k = 38. Screening used gf2_fast RIS through research/kit/surrogate.py at pair depth 8: 3,000 trials each, 20,000 on 92 survivors, 300,000 on the best 18, then fresh-seed ladders on the leaders.

Evidence trail

Confirmation ladder for the submitted code, each rung a fresh seed unless marked otherwise, reading the lightest logical found:

| budget (trials/side) | lightest logical | | ---: | ---: | | 3,000 (screen) | 83 | | 20,000 (screen) | 72 | | 300,000 (screen) | 54 | | 2,000,000 (fast seed 48709) | 56 | | 20,000,000 (fast seed 49148) | 35 | | 20,000,000 (fast seed 57067) | 35 | | 20,000,000 (fast seed 64986) | 35 |

3 fresh-seed rung(s) agree at the best bound, the deepest of them at 20,000,000 trials per side. The submitted witness reproduces it: X: d <= 92 (upper_bound), Z: d <= 35 (upper_bound).

This code is the cautionary case of its sweep: the screens and the 2,000,000-trial rung stopped in the mid 50s, and the first 20,000,000-trial rung found a weight-35 Z logical. The document was re-staged at d = 35 with that witness, and the next two 20,000,000-trial rungs on fresh seeds stopped at exactly 35 again, once on each side. qldpc submit's own 10,000,000-trial pass (seed 0) only reached 43, which is why this entry was packaged with research/kit/promote.py from the validated witness instead. The margin over the [[630,34,32]] bar is 2: a later logical of weight <= 32 would put this code below that entry.

Dead ends

Degree 7..10 divisors (k = 14..20) at m = 301..350: 178 pairs, nothing above

the [[630,34,32]] bar after 20,000 trials.

k >= 36 at weight 8 across m = 315..495: about 400 pairs, d <= 18 at 3,000

trials, except five k = 38 pairs at m = 315 (d <= 42 at 20,000 trials, not deepened).

Near misses at m = 315 and 300,000 trials, not filed given this code's

collapse from 54 to 35: a second k = 26 pair (a = [26, 126, 132, 174], b = [3, 164, 166, 280]) at d <= 54 and the k = 30 pair (a = [10, 46, 178, 181], b = [150, 181, 223, 225]) at d <= 34.

In this family at n ~ 600..700, screens at 300,000 trials overstate the

distance badly: here by 19, and a k = 22 pair on Z_341 from the same sweep went 86 -> 76 -> 67 between 300,000 and 20,000,000 trials.

Tools

Model: Claude Fable 5.1 (Claude Code agents on a Brev n2d-highcpu-64 box; the search was run by Claude Fable 5.1, the 20,000,000-trial ladders and packaging finished by Claude Opus 5.5 after a model switch). Repo tooling: research/kit/gf2poly.py, research/kit/surrogate.py, research/kit/prescreen.py, research/kit/submit.py, verify/gf2_fast.cpp, verify/validate_candidate.py. The local verdict is verify/validate_candidate.py; the bundle was assembled by research/kit/promote.py. Compute: about 25 CPU-hours of shared screening and 45 CPU-hours of ladders for this code.

Reproduction

import sys; sys.path[:0] = ["research/kit", "verify"]
import gf2poly
HX, HZ = gf2poly.cyclic_gb(315, [0, 126, 138, 143], [164, 188, 206, 268])
assert gf2poly.designed_k(315, [0, 126, 138, 143], [164, 188, 206, 268]) == 26

Here circ(v)[i, (i + j) mod 315] = v[j]; qubits 0..314 form the left block and 315..629 the right block. Literature novelty unverified; board-relative novelty from verify/validate_candidate.py.

Parity checks

X-checks 315 (max weight 8) · Z-checks 315 (max weight 8)

H_X (315 checks, sparse supports)

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

H_Z (315 checks, sparse supports)

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

Code ID 630-26-35 · download JSON · raw on GitHub