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[[254,70,18]] d ≤
n
254
k
70
d
18
kd²/n
89.291
w
18
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 18, d_Z ≤ 18 · w_X = 18, w_Z = 18 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 18 · witness weight 18 (claimed upper_bound)
witness operator (support, 18 qubits)
[1, 15, 31, 45, 53, 64, 89, 118, 133, 152, 173, 182, 191, 192, 238, 240, 250, 252]
d_Z 18 · witness weight 18 (claimed upper_bound)
witness found by @vprusso · verify/ris_gpu.py recover mode, pair depth 0 (GPU RIS, CPU re-verified) · found at 3×108 trials · survived 3×108 trials · 2026-09-25
witness operator (support, 18 qubits)
[0, 9, 18, 39, 58, 66, 68, 78, 80, 126, 127, 138, 146, 160, 176, 190, 200, 229]
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 18 · H_Z 18
qubit degrees H_X 9 · H_Z 9
trapping sets H_X (1,9)×254 (2,10)×254 (3,11)×127 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,9): 254 (2,10): 254 (2,14): 3810 (2,16): 10795 (3,11): 127 (3,13): 889 (3,15): 8890 (3,17): 44450 (3,19): 133985 (3,21): 420370 (3,23): 515112 (3,25): 17399
trapping sets H_Z (1,9)×254 (2,10)×254 (3,11)×127 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,9): 254 (2,10): 254 (2,14): 3810 (2,16): 10795 (3,11): 127 (3,13): 889 (3,15): 8890 (3,17): 44450 (3,19): 133985 (3,21): 420370 (3,23): 515112 (3,25): 17399

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction Cyclic generalized bicycle over Z_127 (n=2m=254): H_X=[circ(a)|circ(b)], H_Z=[circ(b)^T|circ(a)^T]. a and b are sparse multiples of the BCH-designed divisor g(x) of x^m-1 (g_int=62504535161; zero-set run 3, complement run 8), found by Prange search inside the ideal (g). Zero-set design after arXiv:2609.22503 (BCH run-length floors); construction family per arXiv:1904.02703. a=[1, 4, 10, 23, 48, 68, 101, 107, 126]; b=[19, 28, 57, 63, 84, 90, 101, 106, 121].
model GLM 5.3 Flash (Zed agent) (claimed, not verified)
date 2026-09-22
notes The search_budget tool string names cyclic_defining_set.py under a research/ path; that script is kept in the authors' own repo and is not a file of this repository.
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

[[254,70,18]]: distance revision of the board's [[254,70,18]] entry

Revision history

The entry keeps its parameters [[254,70,18]]. The code, its checks, its layout, and its original provenance are unchanged; only the distance block is corrected. A GPU random-information-set search (verify/ris_gpu.py, recover mode, 300,000,000 trials per side, pair depth 0, seed 4101) exhibits a weight-18 Z logical, so the previous witness-backed bound was overstated on that side; the overall distance d = 18 is unchanged. Each lighter witness is carried in the entry with the budget it was found at; the other side keeps its original witness where it was not refuted. Distance remains an upper bound, not an exact claim.

Evidence

Every GPU proposal was re-validated on the CPU against the committed check matrices (in the kernel of the opposite side's checks, outside the row space of its own side) before it was recorded. The pass is the weekly fresh-seed re-measurement of the board's cell leaders (issue 2025, run of 2026-09-24); every recorded reading is the lightest CPU-verified logical at that budget.

| side | seed | claimed | GPU best weight | CPU-verified witness | trials | |---|---|---|---|---|---| | X | 4101 | 18 | 18 | 18 | 300,000,000 | | Z | 4101 | 20 | 18 | 18 | 300,000,000 | | X | 4102 | 18 | 18 | 18 | 300,000,000 | | Z | 4102 | 20 | 18 | 18 | 300,000,000 |

Original note, with the file paths updated

[[254,70,18]] — BCH-designed cyclic generalized bicycle over Z_127

Direction & hypothesis

Target cell: unrestricted / any-weight (the code has no 2D layout; its combinatorial locality is not the board's geometric locality). Family: cyclic generalized bicycle over Z_127 (arXiv:1904.02703), the family that produced the board's top kd^2/n codes at n ~ 670-680. The opening this campaign aimed at: choose the common divisor g(x) of x^127-1 by its zero-set structure rather than uniformly, a defining-set idea transferred from arXiv:2609.22503 (optimal dual-containing cyclic LRCs). That paper's q-ary families cannot be binary (their Euclidean case needs (r+delta-1) | (q-1), impossible at q = 2), but one ingredient transfers provably: by the BCH bound, every nonzero multiple of g has Hamming weight >= s+1, where s is the longest run of consecutive exponents in the zero set Z(g) = {i : g(w^i) = 0}. The sparse cofactors h_a = a/g and h_b = b/g are exactly such multiples, so the run length is a zero-cost feasibility filter: an ideal whose zero set contains a run of length >= the target cofactor weight cannot yield a sparse cofactor at all, and the Prange search can be skipped entirely. Dually (Lemma 2.2 there), a run of length t in the complement of Z(gcd(b, x^m-1)) floors every pure-type X-logical (c, 0) in ker(B) at t+1; that complement run (8 here) was used only as a ranking prior, never as a distance claim.

What was searched

One sweep over divisor ideals of x^m - 1 for m in {127, 251, 257, 331, 337} (n = 2m in 254..674), degree targets matched to k = 2 deg(g) bands, cofactor weight band 4-9 (check weight <= 18). Ideals were enumerated as products of irreducible factors of x^m - 1; each ideal's zero set was computed exactly by evaluating g at the m-th roots of unity in GF(2^e) (e = ord_m(2), carryless arithmetic), and ideals whose zero-run exceeded the band were pruned before any search ran. Surviving ideals got a 4000-trial Prange search for sparse cofactors; pairs of cofactors built cyclic GB codes (H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T]), screened at 1200 RIS trials/side, and every screen-surviving code that was nondominated against the full board was deep-confirmed at 100,000 RIS trials/side. 29 records were staged; the 10 mutually non-dominating ones are being submitted, this code among them. The sweep took ~92 min wall clock; the zero-run filter pruned all k = 126/168 cells and all of m in {251, 257, 331} (coset degrees 50/16/30 do not match the swept degree grid) without spending a single search trial on them.

Evidence trail

Ladder for this code: screen 1200 trials/side -> deep confirm 100,000 trials/side -> d <= 18; the submission's own witness search (20,000 RIS trials/side plus a 1,000,000-trial gf2_fast accelerator pass, seed 0) returned the claimed bound d <= 18, with an explicit witness on each side recorded in the submission JSON. The claim is a witness-backed upper bound, not an exact distance; the trusted gate (verify/validate_candidate.py via ./qldpc submit) passed it locally, and CI re-runs the refutation with a fresh seed. Screen values at 1200 trials ran ~5-8% above the 100k deep values (e.g. 112 -> 104 on a sibling record), consistent with the repo's distance-inflation fieldnotes; the submitted claim is the deepest search's.

Near-misses from the same ideal family collapsed under deepening: several [[674,44,<=112]]-screen siblings fell to d <= 104-108, and the k = 126/168 cells at n = 254/674 collapsed to d <= 8 (rate too high for the blocklength).

Dead ends

  • m = 251, 257, 331 produced nothing: their cyclotomic-coset degrees

    • (50, 16, 30) do not divide the swept degree targets, so every degree grid was empty. The feasibility filter made this costless; the lesson is to scale the degree grid by e = ord_m(2) per m.

  • High-rate cells (k = 2m/4 and above at these m) give d <= 8 across the

    • board: the BCH run-length filter admits cofactors there, but the quantum distance collapses.

  • The q-ary constructions of arXiv:2609.22503 themselves: no binary entry

    • exists (Euclidean families need (r+delta-1) | (q-1); the Hermitian q = 2 corner gives only n = 3u or 5u codes with d <= 6), so only the zero-set design principle was portable.

Tools

Model: GLM 5.3 Flash (Zed agent). Harness: research/kit (css, surrogate, gf2_fast accelerator) plus a new constructor module implementing the GF(2^e) zero-set evaluation, the BCH feasibility filter, and the sweep driver; packaging and gating through ./qldpc submit (20k RIS + 1M accelerator trials, then the full local verifier). Compute: ~92 min sweep + per-code deep confirms, on a machine shared with two concurrent campaigns (timings inflated).

Reproduction

Build the circulants over Z_127: A = circ(a), B = circ(b) with first rows a = [1, 4, 10, 23, 48, 68, 101, 107, 126] and b = [19, 28, 57, 63, 84, 90, 101, 106, 121] (0/1 vectors of length 127, ones at the listed indices), then H_X = [A | B] and H_Z = [B^T | A^T]. The common divisor is g_int = 62504535161 (little-endian coefficient bitmask of g(x) | x^127 - 1), of degree 35; its zero set has longest consecutive run 3 and its complement 8, so the BCH floor on any cofactor is 4 and the pure-logical floor through ker(B) is 9. The cofactors above are multiples of g mod x^127 - 1; k = 2 deg(g) = 70. The sweep method (GF(2^e) zero-set evaluation, BCH feasibility filter, Prange inside the ideal) is described in full above; the parameters in this section rebuild (H_X, H_Z) directly.

Parity checks

X-checks 127 (max weight 18) · Z-checks 127 (max weight 18)
H_X (127 checks, sparse supports)
[1, 4, 10, 23, 48, 68, 101, 107, 126, 146, 155, 184, 190, 211, 217, 228, 233, 248] [0, 2, 5, 11, 24, 49, 69, 102, 108, 147, 156, 185, 191, 212, 218, 229, 234, 249] [1, 3, 6, 12, 25, 50, 70, 103, 109, 148, 157, 186, 192, 213, 219, 230, 235, 250] [2, 4, 7, 13, 26, 51, 71, 104, 110, 149, 158, 187, 193, 214, 220, 231, 236, 251] [3, 5, 8, 14, 27, 52, 72, 105, 111, 150, 159, 188, 194, 215, 221, 232, 237, 252] [4, 6, 9, 15, 28, 53, 73, 106, 112, 151, 160, 189, 195, 216, 222, 233, 238, 253] [5, 7, 10, 16, 29, 54, 74, 107, 113, 127, 152, 161, 190, 196, 217, 223, 234, 239] [6, 8, 11, 17, 30, 55, 75, 108, 114, 128, 153, 162, 191, 197, 218, 224, 235, 240] [7, 9, 12, 18, 31, 56, 76, 109, 115, 129, 154, 163, 192, 198, 219, 225, 236, 241] [8, 10, 13, 19, 32, 57, 77, 110, 116, 130, 155, 164, 193, 199, 220, 226, 237, 242] [9, 11, 14, 20, 33, 58, 78, 111, 117, 131, 156, 165, 194, 200, 221, 227, 238, 243] [10, 12, 15, 21, 34, 59, 79, 112, 118, 132, 157, 166, 195, 201, 222, 228, 239, 244] [11, 13, 16, 22, 35, 60, 80, 113, 119, 133, 158, 167, 196, 202, 223, 229, 240, 245] [12, 14, 17, 23, 36, 61, 81, 114, 120, 134, 159, 168, 197, 203, 224, 230, 241, 246] [13, 15, 18, 24, 37, 62, 82, 115, 121, 135, 160, 169, 198, 204, 225, 231, 242, 247] [14, 16, 19, 25, 38, 63, 83, 116, 122, 136, 161, 170, 199, 205, 226, 232, 243, 248] [15, 17, 20, 26, 39, 64, 84, 117, 123, 137, 162, 171, 200, 206, 227, 233, 244, 249] [16, 18, 21, 27, 40, 65, 85, 118, 124, 138, 163, 172, 201, 207, 228, 234, 245, 250] [17, 19, 22, 28, 41, 66, 86, 119, 125, 139, 164, 173, 202, 208, 229, 235, 246, 251] [18, 20, 23, 29, 42, 67, 87, 120, 126, 140, 165, 174, 203, 209, 230, 236, 247, 252] [0, 19, 21, 24, 30, 43, 68, 88, 121, 141, 166, 175, 204, 210, 231, 237, 248, 253] [1, 20, 22, 25, 31, 44, 69, 89, 122, 127, 142, 167, 176, 205, 211, 232, 238, 249] [2, 21, 23, 26, 32, 45, 70, 90, 123, 128, 143, 168, 177, 206, 212, 233, 239, 250] [3, 22, 24, 27, 33, 46, 71, 91, 124, 129, 144, 169, 178, 207, 213, 234, 240, 251] [4, 23, 25, 28, 34, 47, 72, 92, 125, 130, 145, 170, 179, 208, 214, 235, 241, 252] [5, 24, 26, 29, 35, 48, 73, 93, 126, 131, 146, 171, 180, 209, 215, 236, 242, 253] [0, 6, 25, 27, 30, 36, 49, 74, 94, 127, 132, 147, 172, 181, 210, 216, 237, 243] [1, 7, 26, 28, 31, 37, 50, 75, 95, 128, 133, 148, 173, 182, 211, 217, 238, 244] [2, 8, 27, 29, 32, 38, 51, 76, 96, 129, 134, 149, 174, 183, 212, 218, 239, 245] [3, 9, 28, 30, 33, 39, 52, 77, 97, 130, 135, 150, 175, 184, 213, 219, 240, 246] [4, 10, 29, 31, 34, 40, 53, 78, 98, 131, 136, 151, 176, 185, 214, 220, 241, 247] [5, 11, 30, 32, 35, 41, 54, 79, 99, 132, 137, 152, 177, 186, 215, 221, 242, 248] [6, 12, 31, 33, 36, 42, 55, 80, 100, 133, 138, 153, 178, 187, 216, 222, 243, 249] [7, 13, 32, 34, 37, 43, 56, 81, 101, 134, 139, 154, 179, 188, 217, 223, 244, 250] [8, 14, 33, 35, 38, 44, 57, 82, 102, 135, 140, 155, 180, 189, 218, 224, 245, 251] [9, 15, 34, 36, 39, 45, 58, 83, 103, 136, 141, 156, 181, 190, 219, 225, 246, 252] [10, 16, 35, 37, 40, 46, 59, 84, 104, 137, 142, 157, 182, 191, 220, 226, 247, 253] [11, 17, 36, 38, 41, 47, 60, 85, 105, 127, 138, 143, 158, 183, 192, 221, 227, 248] [12, 18, 37, 39, 42, 48, 61, 86, 106, 128, 139, 144, 159, 184, 193, 222, 228, 249] [13, 19, 38, 40, 43, 49, 62, 87, 107, 129, 140, 145, 160, 185, 194, 223, 229, 250] [14, 20, 39, 41, 44, 50, 63, 88, 108, 130, 141, 146, 161, 186, 195, 224, 230, 251] [15, 21, 40, 42, 45, 51, 64, 89, 109, 131, 142, 147, 162, 187, 196, 225, 231, 252] [16, 22, 41, 43, 46, 52, 65, 90, 110, 132, 143, 148, 163, 188, 197, 226, 232, 253] [17, 23, 42, 44, 47, 53, 66, 91, 111, 127, 133, 144, 149, 164, 189, 198, 227, 233] [18, 24, 43, 45, 48, 54, 67, 92, 112, 128, 134, 145, 150, 165, 190, 199, 228, 234] [19, 25, 44, 46, 49, 55, 68, 93, 113, 129, 135, 146, 151, 166, 191, 200, 229, 235] [20, 26, 45, 47, 50, 56, 69, 94, 114, 130, 136, 147, 152, 167, 192, 201, 230, 236] [21, 27, 46, 48, 51, 57, 70, 95, 115, 131, 137, 148, 153, 168, 193, 202, 231, 237] [22, 28, 47, 49, 52, 58, 71, 96, 116, 132, 138, 149, 154, 169, 194, 203, 232, 238] [23, 29, 48, 50, 53, 59, 72, 97, 117, 133, 139, 150, 155, 170, 195, 204, 233, 239] [24, 30, 49, 51, 54, 60, 73, 98, 118, 134, 140, 151, 156, 171, 196, 205, 234, 240] [25, 31, 50, 52, 55, 61, 74, 99, 119, 135, 141, 152, 157, 172, 197, 206, 235, 241] [26, 32, 51, 53, 56, 62, 75, 100, 120, 136, 142, 153, 158, 173, 198, 207, 236, 242] [27, 33, 52, 54, 57, 63, 76, 101, 121, 137, 143, 154, 159, 174, 199, 208, 237, 243] [28, 34, 53, 55, 58, 64, 77, 102, 122, 138, 144, 155, 160, 175, 200, 209, 238, 244] [29, 35, 54, 56, 59, 65, 78, 103, 123, 139, 145, 156, 161, 176, 201, 210, 239, 245] [30, 36, 55, 57, 60, 66, 79, 104, 124, 140, 146, 157, 162, 177, 202, 211, 240, 246] [31, 37, 56, 58, 61, 67, 80, 105, 125, 141, 147, 158, 163, 178, 203, 212, 241, 247] [32, 38, 57, 59, 62, 68, 81, 106, 126, 142, 148, 159, 164, 179, 204, 213, 242, 248] [0, 33, 39, 58, 60, 63, 69, 82, 107, 143, 149, 160, 165, 180, 205, 214, 243, 249] [1, 34, 40, 59, 61, 64, 70, 83, 108, 144, 150, 161, 166, 181, 206, 215, 244, 250] [2, 35, 41, 60, 62, 65, 71, 84, 109, 145, 151, 162, 167, 182, 207, 216, 245, 251] [3, 36, 42, 61, 63, 66, 72, 85, 110, 146, 152, 163, 168, 183, 208, 217, 246, 252] [4, 37, 43, 62, 64, 67, 73, 86, 111, 147, 153, 164, 169, 184, 209, 218, 247, 253] [5, 38, 44, 63, 65, 68, 74, 87, 112, 127, 148, 154, 165, 170, 185, 210, 219, 248] [6, 39, 45, 64, 66, 69, 75, 88, 113, 128, 149, 155, 166, 171, 186, 211, 220, 249] [7, 40, 46, 65, 67, 70, 76, 89, 114, 129, 150, 156, 167, 172, 187, 212, 221, 250] [8, 41, 47, 66, 68, 71, 77, 90, 115, 130, 151, 157, 168, 173, 188, 213, 222, 251] [9, 42, 48, 67, 69, 72, 78, 91, 116, 131, 152, 158, 169, 174, 189, 214, 223, 252] [10, 43, 49, 68, 70, 73, 79, 92, 117, 132, 153, 159, 170, 175, 190, 215, 224, 253] [11, 44, 50, 69, 71, 74, 80, 93, 118, 127, 133, 154, 160, 171, 176, 191, 216, 225] [12, 45, 51, 70, 72, 75, 81, 94, 119, 128, 134, 155, 161, 172, 177, 192, 217, 226] [13, 46, 52, 71, 73, 76, 82, 95, 120, 129, 135, 156, 162, 173, 178, 193, 218, 227] [14, 47, 53, 72, 74, 77, 83, 96, 121, 130, 136, 157, 163, 174, 179, 194, 219, 228] [15, 48, 54, 73, 75, 78, 84, 97, 122, 131, 137, 158, 164, 175, 180, 195, 220, 229] [16, 49, 55, 74, 76, 79, 85, 98, 123, 132, 138, 159, 165, 176, 181, 196, 221, 230] [17, 50, 56, 75, 77, 80, 86, 99, 124, 133, 139, 160, 166, 177, 182, 197, 222, 231] [18, 51, 57, 76, 78, 81, 87, 100, 125, 134, 140, 161, 167, 178, 183, 198, 223, 232] [19, 52, 58, 77, 79, 82, 88, 101, 126, 135, 141, 162, 168, 179, 184, 199, 224, 233] [0, 20, 53, 59, 78, 80, 83, 89, 102, 136, 142, 163, 169, 180, 185, 200, 225, 234] [1, 21, 54, 60, 79, 81, 84, 90, 103, 137, 143, 164, 170, 181, 186, 201, 226, 235] [2, 22, 55, 61, 80, 82, 85, 91, 104, 138, 144, 165, 171, 182, 187, 202, 227, 236] [3, 23, 56, 62, 81, 83, 86, 92, 105, 139, 145, 166, 172, 183, 188, 203, 228, 237] [4, 24, 57, 63, 82, 84, 87, 93, 106, 140, 146, 167, 173, 184, 189, 204, 229, 238] [5, 25, 58, 64, 83, 85, 88, 94, 107, 141, 147, 168, 174, 185, 190, 205, 230, 239] [6, 26, 59, 65, 84, 86, 89, 95, 108, 142, 148, 169, 175, 186, 191, 206, 231, 240] [7, 27, 60, 66, 85, 87, 90, 96, 109, 143, 149, 170, 176, 187, 192, 207, 232, 241] [8, 28, 61, 67, 86, 88, 91, 97, 110, 144, 150, 171, 177, 188, 193, 208, 233, 242] [9, 29, 62, 68, 87, 89, 92, 98, 111, 145, 151, 172, 178, 189, 194, 209, 234, 243] [10, 30, 63, 69, 88, 90, 93, 99, 112, 146, 152, 173, 179, 190, 195, 210, 235, 244] [11, 31, 64, 70, 89, 91, 94, 100, 113, 147, 153, 174, 180, 191, 196, 211, 236, 245] [12, 32, 65, 71, 90, 92, 95, 101, 114, 148, 154, 175, 181, 192, 197, 212, 237, 246] [13, 33, 66, 72, 91, 93, 96, 102, 115, 149, 155, 176, 182, 193, 198, 213, 238, 247] [14, 34, 67, 73, 92, 94, 97, 103, 116, 150, 156, 177, 183, 194, 199, 214, 239, 248] [15, 35, 68, 74, 93, 95, 98, 104, 117, 151, 157, 178, 184, 195, 200, 215, 240, 249] [16, 36, 69, 75, 94, 96, 99, 105, 118, 152, 158, 179, 185, 196, 201, 216, 241, 250] [17, 37, 70, 76, 95, 97, 100, 106, 119, 153, 159, 180, 186, 197, 202, 217, 242, 251] [18, 38, 71, 77, 96, 98, 101, 107, 120, 154, 160, 181, 187, 198, 203, 218, 243, 252] [19, 39, 72, 78, 97, 99, 102, 108, 121, 155, 161, 182, 188, 199, 204, 219, 244, 253] [20, 40, 73, 79, 98, 100, 103, 109, 122, 127, 156, 162, 183, 189, 200, 205, 220, 245] [21, 41, 74, 80, 99, 101, 104, 110, 123, 128, 157, 163, 184, 190, 201, 206, 221, 246] [22, 42, 75, 81, 100, 102, 105, 111, 124, 129, 158, 164, 185, 191, 202, 207, 222, 247] [23, 43, 76, 82, 101, 103, 106, 112, 125, 130, 159, 165, 186, 192, 203, 208, 223, 248] [24, 44, 77, 83, 102, 104, 107, 113, 126, 131, 160, 166, 187, 193, 204, 209, 224, 249] [0, 25, 45, 78, 84, 103, 105, 108, 114, 132, 161, 167, 188, 194, 205, 210, 225, 250] [1, 26, 46, 79, 85, 104, 106, 109, 115, 133, 162, 168, 189, 195, 206, 211, 226, 251] [2, 27, 47, 80, 86, 105, 107, 110, 116, 134, 163, 169, 190, 196, 207, 212, 227, 252] [3, 28, 48, 81, 87, 106, 108, 111, 117, 135, 164, 170, 191, 197, 208, 213, 228, 253] [4, 29, 49, 82, 88, 107, 109, 112, 118, 127, 136, 165, 171, 192, 198, 209, 214, 229] [5, 30, 50, 83, 89, 108, 110, 113, 119, 128, 137, 166, 172, 193, 199, 210, 215, 230] [6, 31, 51, 84, 90, 109, 111, 114, 120, 129, 138, 167, 173, 194, 200, 211, 216, 231] [7, 32, 52, 85, 91, 110, 112, 115, 121, 130, 139, 168, 174, 195, 201, 212, 217, 232] [8, 33, 53, 86, 92, 111, 113, 116, 122, 131, 140, 169, 175, 196, 202, 213, 218, 233] [9, 34, 54, 87, 93, 112, 114, 117, 123, 132, 141, 170, 176, 197, 203, 214, 219, 234] [10, 35, 55, 88, 94, 113, 115, 118, 124, 133, 142, 171, 177, 198, 204, 215, 220, 235] [11, 36, 56, 89, 95, 114, 116, 119, 125, 134, 143, 172, 178, 199, 205, 216, 221, 236] [12, 37, 57, 90, 96, 115, 117, 120, 126, 135, 144, 173, 179, 200, 206, 217, 222, 237] [0, 13, 38, 58, 91, 97, 116, 118, 121, 136, 145, 174, 180, 201, 207, 218, 223, 238] [1, 14, 39, 59, 92, 98, 117, 119, 122, 137, 146, 175, 181, 202, 208, 219, 224, 239] [2, 15, 40, 60, 93, 99, 118, 120, 123, 138, 147, 176, 182, 203, 209, 220, 225, 240] [3, 16, 41, 61, 94, 100, 119, 121, 124, 139, 148, 177, 183, 204, 210, 221, 226, 241] [4, 17, 42, 62, 95, 101, 120, 122, 125, 140, 149, 178, 184, 205, 211, 222, 227, 242] [5, 18, 43, 63, 96, 102, 121, 123, 126, 141, 150, 179, 185, 206, 212, 223, 228, 243] [0, 6, 19, 44, 64, 97, 103, 122, 124, 142, 151, 180, 186, 207, 213, 224, 229, 244] [1, 7, 20, 45, 65, 98, 104, 123, 125, 143, 152, 181, 187, 208, 214, 225, 230, 245] [2, 8, 21, 46, 66, 99, 105, 124, 126, 144, 153, 182, 188, 209, 215, 226, 231, 246] [0, 3, 9, 22, 47, 67, 100, 106, 125, 145, 154, 183, 189, 210, 216, 227, 232, 247]
H_Z (127 checks, sparse supports)
[6, 21, 26, 37, 43, 64, 70, 99, 108, 128, 147, 153, 186, 206, 231, 244, 250, 253] [7, 22, 27, 38, 44, 65, 71, 100, 109, 127, 129, 148, 154, 187, 207, 232, 245, 251] [8, 23, 28, 39, 45, 66, 72, 101, 110, 128, 130, 149, 155, 188, 208, 233, 246, 252] [9, 24, 29, 40, 46, 67, 73, 102, 111, 129, 131, 150, 156, 189, 209, 234, 247, 253] [10, 25, 30, 41, 47, 68, 74, 103, 112, 127, 130, 132, 151, 157, 190, 210, 235, 248] [11, 26, 31, 42, 48, 69, 75, 104, 113, 128, 131, 133, 152, 158, 191, 211, 236, 249] [12, 27, 32, 43, 49, 70, 76, 105, 114, 129, 132, 134, 153, 159, 192, 212, 237, 250] [13, 28, 33, 44, 50, 71, 77, 106, 115, 130, 133, 135, 154, 160, 193, 213, 238, 251] [14, 29, 34, 45, 51, 72, 78, 107, 116, 131, 134, 136, 155, 161, 194, 214, 239, 252] [15, 30, 35, 46, 52, 73, 79, 108, 117, 132, 135, 137, 156, 162, 195, 215, 240, 253] [16, 31, 36, 47, 53, 74, 80, 109, 118, 127, 133, 136, 138, 157, 163, 196, 216, 241] [17, 32, 37, 48, 54, 75, 81, 110, 119, 128, 134, 137, 139, 158, 164, 197, 217, 242] [18, 33, 38, 49, 55, 76, 82, 111, 120, 129, 135, 138, 140, 159, 165, 198, 218, 243] [19, 34, 39, 50, 56, 77, 83, 112, 121, 130, 136, 139, 141, 160, 166, 199, 219, 244] [20, 35, 40, 51, 57, 78, 84, 113, 122, 131, 137, 140, 142, 161, 167, 200, 220, 245] [21, 36, 41, 52, 58, 79, 85, 114, 123, 132, 138, 141, 143, 162, 168, 201, 221, 246] [22, 37, 42, 53, 59, 80, 86, 115, 124, 133, 139, 142, 144, 163, 169, 202, 222, 247] [23, 38, 43, 54, 60, 81, 87, 116, 125, 134, 140, 143, 145, 164, 170, 203, 223, 248] [24, 39, 44, 55, 61, 82, 88, 117, 126, 135, 141, 144, 146, 165, 171, 204, 224, 249] [0, 25, 40, 45, 56, 62, 83, 89, 118, 136, 142, 145, 147, 166, 172, 205, 225, 250] [1, 26, 41, 46, 57, 63, 84, 90, 119, 137, 143, 146, 148, 167, 173, 206, 226, 251] [2, 27, 42, 47, 58, 64, 85, 91, 120, 138, 144, 147, 149, 168, 174, 207, 227, 252] [3, 28, 43, 48, 59, 65, 86, 92, 121, 139, 145, 148, 150, 169, 175, 208, 228, 253] [4, 29, 44, 49, 60, 66, 87, 93, 122, 127, 140, 146, 149, 151, 170, 176, 209, 229] [5, 30, 45, 50, 61, 67, 88, 94, 123, 128, 141, 147, 150, 152, 171, 177, 210, 230] [6, 31, 46, 51, 62, 68, 89, 95, 124, 129, 142, 148, 151, 153, 172, 178, 211, 231] [7, 32, 47, 52, 63, 69, 90, 96, 125, 130, 143, 149, 152, 154, 173, 179, 212, 232] [8, 33, 48, 53, 64, 70, 91, 97, 126, 131, 144, 150, 153, 155, 174, 180, 213, 233] [0, 9, 34, 49, 54, 65, 71, 92, 98, 132, 145, 151, 154, 156, 175, 181, 214, 234] [1, 10, 35, 50, 55, 66, 72, 93, 99, 133, 146, 152, 155, 157, 176, 182, 215, 235] [2, 11, 36, 51, 56, 67, 73, 94, 100, 134, 147, 153, 156, 158, 177, 183, 216, 236] [3, 12, 37, 52, 57, 68, 74, 95, 101, 135, 148, 154, 157, 159, 178, 184, 217, 237] [4, 13, 38, 53, 58, 69, 75, 96, 102, 136, 149, 155, 158, 160, 179, 185, 218, 238] [5, 14, 39, 54, 59, 70, 76, 97, 103, 137, 150, 156, 159, 161, 180, 186, 219, 239] [6, 15, 40, 55, 60, 71, 77, 98, 104, 138, 151, 157, 160, 162, 181, 187, 220, 240] [7, 16, 41, 56, 61, 72, 78, 99, 105, 139, 152, 158, 161, 163, 182, 188, 221, 241] [8, 17, 42, 57, 62, 73, 79, 100, 106, 140, 153, 159, 162, 164, 183, 189, 222, 242] [9, 18, 43, 58, 63, 74, 80, 101, 107, 141, 154, 160, 163, 165, 184, 190, 223, 243] [10, 19, 44, 59, 64, 75, 81, 102, 108, 142, 155, 161, 164, 166, 185, 191, 224, 244] [11, 20, 45, 60, 65, 76, 82, 103, 109, 143, 156, 162, 165, 167, 186, 192, 225, 245] [12, 21, 46, 61, 66, 77, 83, 104, 110, 144, 157, 163, 166, 168, 187, 193, 226, 246] [13, 22, 47, 62, 67, 78, 84, 105, 111, 145, 158, 164, 167, 169, 188, 194, 227, 247] [14, 23, 48, 63, 68, 79, 85, 106, 112, 146, 159, 165, 168, 170, 189, 195, 228, 248] [15, 24, 49, 64, 69, 80, 86, 107, 113, 147, 160, 166, 169, 171, 190, 196, 229, 249] [16, 25, 50, 65, 70, 81, 87, 108, 114, 148, 161, 167, 170, 172, 191, 197, 230, 250] [17, 26, 51, 66, 71, 82, 88, 109, 115, 149, 162, 168, 171, 173, 192, 198, 231, 251] [18, 27, 52, 67, 72, 83, 89, 110, 116, 150, 163, 169, 172, 174, 193, 199, 232, 252] [19, 28, 53, 68, 73, 84, 90, 111, 117, 151, 164, 170, 173, 175, 194, 200, 233, 253] [20, 29, 54, 69, 74, 85, 91, 112, 118, 127, 152, 165, 171, 174, 176, 195, 201, 234] [21, 30, 55, 70, 75, 86, 92, 113, 119, 128, 153, 166, 172, 175, 177, 196, 202, 235] [22, 31, 56, 71, 76, 87, 93, 114, 120, 129, 154, 167, 173, 176, 178, 197, 203, 236] [23, 32, 57, 72, 77, 88, 94, 115, 121, 130, 155, 168, 174, 177, 179, 198, 204, 237] [24, 33, 58, 73, 78, 89, 95, 116, 122, 131, 156, 169, 175, 178, 180, 199, 205, 238] [25, 34, 59, 74, 79, 90, 96, 117, 123, 132, 157, 170, 176, 179, 181, 200, 206, 239] [26, 35, 60, 75, 80, 91, 97, 118, 124, 133, 158, 171, 177, 180, 182, 201, 207, 240] [27, 36, 61, 76, 81, 92, 98, 119, 125, 134, 159, 172, 178, 181, 183, 202, 208, 241] [28, 37, 62, 77, 82, 93, 99, 120, 126, 135, 160, 173, 179, 182, 184, 203, 209, 242] [0, 29, 38, 63, 78, 83, 94, 100, 121, 136, 161, 174, 180, 183, 185, 204, 210, 243] [1, 30, 39, 64, 79, 84, 95, 101, 122, 137, 162, 175, 181, 184, 186, 205, 211, 244] [2, 31, 40, 65, 80, 85, 96, 102, 123, 138, 163, 176, 182, 185, 187, 206, 212, 245] [3, 32, 41, 66, 81, 86, 97, 103, 124, 139, 164, 177, 183, 186, 188, 207, 213, 246] [4, 33, 42, 67, 82, 87, 98, 104, 125, 140, 165, 178, 184, 187, 189, 208, 214, 247] [5, 34, 43, 68, 83, 88, 99, 105, 126, 141, 166, 179, 185, 188, 190, 209, 215, 248] [0, 6, 35, 44, 69, 84, 89, 100, 106, 142, 167, 180, 186, 189, 191, 210, 216, 249] [1, 7, 36, 45, 70, 85, 90, 101, 107, 143, 168, 181, 187, 190, 192, 211, 217, 250] [2, 8, 37, 46, 71, 86, 91, 102, 108, 144, 169, 182, 188, 191, 193, 212, 218, 251] [3, 9, 38, 47, 72, 87, 92, 103, 109, 145, 170, 183, 189, 192, 194, 213, 219, 252] [4, 10, 39, 48, 73, 88, 93, 104, 110, 146, 171, 184, 190, 193, 195, 214, 220, 253] [5, 11, 40, 49, 74, 89, 94, 105, 111, 127, 147, 172, 185, 191, 194, 196, 215, 221] [6, 12, 41, 50, 75, 90, 95, 106, 112, 128, 148, 173, 186, 192, 195, 197, 216, 222] [7, 13, 42, 51, 76, 91, 96, 107, 113, 129, 149, 174, 187, 193, 196, 198, 217, 223] [8, 14, 43, 52, 77, 92, 97, 108, 114, 130, 150, 175, 188, 194, 197, 199, 218, 224] [9, 15, 44, 53, 78, 93, 98, 109, 115, 131, 151, 176, 189, 195, 198, 200, 219, 225] [10, 16, 45, 54, 79, 94, 99, 110, 116, 132, 152, 177, 190, 196, 199, 201, 220, 226] [11, 17, 46, 55, 80, 95, 100, 111, 117, 133, 153, 178, 191, 197, 200, 202, 221, 227] [12, 18, 47, 56, 81, 96, 101, 112, 118, 134, 154, 179, 192, 198, 201, 203, 222, 228] [13, 19, 48, 57, 82, 97, 102, 113, 119, 135, 155, 180, 193, 199, 202, 204, 223, 229] [14, 20, 49, 58, 83, 98, 103, 114, 120, 136, 156, 181, 194, 200, 203, 205, 224, 230] [15, 21, 50, 59, 84, 99, 104, 115, 121, 137, 157, 182, 195, 201, 204, 206, 225, 231] [16, 22, 51, 60, 85, 100, 105, 116, 122, 138, 158, 183, 196, 202, 205, 207, 226, 232] [17, 23, 52, 61, 86, 101, 106, 117, 123, 139, 159, 184, 197, 203, 206, 208, 227, 233] [18, 24, 53, 62, 87, 102, 107, 118, 124, 140, 160, 185, 198, 204, 207, 209, 228, 234] [19, 25, 54, 63, 88, 103, 108, 119, 125, 141, 161, 186, 199, 205, 208, 210, 229, 235] [20, 26, 55, 64, 89, 104, 109, 120, 126, 142, 162, 187, 200, 206, 209, 211, 230, 236] [0, 21, 27, 56, 65, 90, 105, 110, 121, 143, 163, 188, 201, 207, 210, 212, 231, 237] [1, 22, 28, 57, 66, 91, 106, 111, 122, 144, 164, 189, 202, 208, 211, 213, 232, 238] [2, 23, 29, 58, 67, 92, 107, 112, 123, 145, 165, 190, 203, 209, 212, 214, 233, 239] [3, 24, 30, 59, 68, 93, 108, 113, 124, 146, 166, 191, 204, 210, 213, 215, 234, 240] [4, 25, 31, 60, 69, 94, 109, 114, 125, 147, 167, 192, 205, 211, 214, 216, 235, 241] [5, 26, 32, 61, 70, 95, 110, 115, 126, 148, 168, 193, 206, 212, 215, 217, 236, 242] [0, 6, 27, 33, 62, 71, 96, 111, 116, 149, 169, 194, 207, 213, 216, 218, 237, 243] [1, 7, 28, 34, 63, 72, 97, 112, 117, 150, 170, 195, 208, 214, 217, 219, 238, 244] [2, 8, 29, 35, 64, 73, 98, 113, 118, 151, 171, 196, 209, 215, 218, 220, 239, 245] [3, 9, 30, 36, 65, 74, 99, 114, 119, 152, 172, 197, 210, 216, 219, 221, 240, 246] [4, 10, 31, 37, 66, 75, 100, 115, 120, 153, 173, 198, 211, 217, 220, 222, 241, 247] [5, 11, 32, 38, 67, 76, 101, 116, 121, 154, 174, 199, 212, 218, 221, 223, 242, 248] [6, 12, 33, 39, 68, 77, 102, 117, 122, 155, 175, 200, 213, 219, 222, 224, 243, 249] [7, 13, 34, 40, 69, 78, 103, 118, 123, 156, 176, 201, 214, 220, 223, 225, 244, 250] [8, 14, 35, 41, 70, 79, 104, 119, 124, 157, 177, 202, 215, 221, 224, 226, 245, 251] [9, 15, 36, 42, 71, 80, 105, 120, 125, 158, 178, 203, 216, 222, 225, 227, 246, 252] [10, 16, 37, 43, 72, 81, 106, 121, 126, 159, 179, 204, 217, 223, 226, 228, 247, 253] [0, 11, 17, 38, 44, 73, 82, 107, 122, 127, 160, 180, 205, 218, 224, 227, 229, 248] [1, 12, 18, 39, 45, 74, 83, 108, 123, 128, 161, 181, 206, 219, 225, 228, 230, 249] [2, 13, 19, 40, 46, 75, 84, 109, 124, 129, 162, 182, 207, 220, 226, 229, 231, 250] [3, 14, 20, 41, 47, 76, 85, 110, 125, 130, 163, 183, 208, 221, 227, 230, 232, 251] [4, 15, 21, 42, 48, 77, 86, 111, 126, 131, 164, 184, 209, 222, 228, 231, 233, 252] [0, 5, 16, 22, 43, 49, 78, 87, 112, 132, 165, 185, 210, 223, 229, 232, 234, 253] [1, 6, 17, 23, 44, 50, 79, 88, 113, 127, 133, 166, 186, 211, 224, 230, 233, 235] [2, 7, 18, 24, 45, 51, 80, 89, 114, 128, 134, 167, 187, 212, 225, 231, 234, 236] [3, 8, 19, 25, 46, 52, 81, 90, 115, 129, 135, 168, 188, 213, 226, 232, 235, 237] [4, 9, 20, 26, 47, 53, 82, 91, 116, 130, 136, 169, 189, 214, 227, 233, 236, 238] [5, 10, 21, 27, 48, 54, 83, 92, 117, 131, 137, 170, 190, 215, 228, 234, 237, 239] [6, 11, 22, 28, 49, 55, 84, 93, 118, 132, 138, 171, 191, 216, 229, 235, 238, 240] [7, 12, 23, 29, 50, 56, 85, 94, 119, 133, 139, 172, 192, 217, 230, 236, 239, 241] [8, 13, 24, 30, 51, 57, 86, 95, 120, 134, 140, 173, 193, 218, 231, 237, 240, 242] [9, 14, 25, 31, 52, 58, 87, 96, 121, 135, 141, 174, 194, 219, 232, 238, 241, 243] [10, 15, 26, 32, 53, 59, 88, 97, 122, 136, 142, 175, 195, 220, 233, 239, 242, 244] [11, 16, 27, 33, 54, 60, 89, 98, 123, 137, 143, 176, 196, 221, 234, 240, 243, 245] [12, 17, 28, 34, 55, 61, 90, 99, 124, 138, 144, 177, 197, 222, 235, 241, 244, 246] [13, 18, 29, 35, 56, 62, 91, 100, 125, 139, 145, 178, 198, 223, 236, 242, 245, 247] [14, 19, 30, 36, 57, 63, 92, 101, 126, 140, 146, 179, 199, 224, 237, 243, 246, 248] [0, 15, 20, 31, 37, 58, 64, 93, 102, 141, 147, 180, 200, 225, 238, 244, 247, 249] [1, 16, 21, 32, 38, 59, 65, 94, 103, 142, 148, 181, 201, 226, 239, 245, 248, 250] [2, 17, 22, 33, 39, 60, 66, 95, 104, 143, 149, 182, 202, 227, 240, 246, 249, 251] [3, 18, 23, 34, 40, 61, 67, 96, 105, 144, 150, 183, 203, 228, 241, 247, 250, 252] [4, 19, 24, 35, 41, 62, 68, 97, 106, 145, 151, 184, 204, 229, 242, 248, 251, 253] [5, 20, 25, 36, 42, 63, 69, 98, 107, 127, 146, 152, 185, 205, 230, 243, 249, 252]
Code ID 254-70-18 · download JSON · raw on GitHub