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[[492,8,20]] d ≤
n
492
k
8
d
20
kd²/n
6.504
w
8
X/Z
1
g
0.102
r
4.0
layers
1
swaps
903

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Distance

X/Z asymmetry 1 · d_X ≤ 20, d_Z ≤ 20 · 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 20 · witness weight 20 (claimed upper_bound)
witness operator (support, 20 qubits)
[19, 35, 66, 82, 83, 131, 215, 270, 286, 318, 319, 334, 335, 351, 366, 414, 432, 446, 447, 449]
d_Z 20 · witness weight 20 (claimed upper_bound)
witness operator (support, 20 qubits)
[177, 194, 204, 205, 214, 217, 218, 228, 231, 426, 427, 440, 441, 443, 452, 454, 456, 457, 462, 479]
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 2–8 (mean 6.869) · H_Z 2–8 (mean 7.109)
qubit degrees H_X 1–6 (mean 3.616) · H_Z 1–4 (mean 3.453)
trapping sets H_X (1,1)×36 (2,0)×7 (3,0)×23 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 36 (1,2): 48 (1,3): 41 (1,4): 323 (1,5): 32 (1,6): 12 (2,0): 7 (2,1): 84 (2,2): 154 (2,3): 308 (2,4): 989 (2,5): 335 (2,6): 2407 (2,7): 138 (2,8): 198 (2,9): 39 (3,0): 23 (3,1): 140 (3,2): 510 (3,3): 1427 (3,4): 3288 (3,5): 4171 (3,6): 17019 (3,7): 4329 (3,8): 27023 (3,9): 2026 (3,10): 3650 (3,11): 800 (3,12): 336 (3,13): 81
trapping sets H_Z (1,1)×48 (2,0)×28 (3,0)×10 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 48 (1,2): 38 (1,3): 49 (1,4): 357 (2,0): 28 (2,1): 88 (2,2): 147 (2,3): 322 (2,4): 1046 (2,5): 344 (2,6): 2645 (3,0): 10 (3,1): 175 (3,2): 634 (3,3): 1466 (3,4): 3323 (3,5): 4513 (3,6): 18368 (3,7): 4091 (3,8): 29188 (3,9): 257 (3,10): 1955
witness diameter X 18.3848 · Z 20.0 (Euclidean support diameter of the stored distance witnesses in the layout; an upper bound on the exhibited logicals’ spread, not a minimum over all logicals)

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 4
X checkZ checkqubit site (492)dashed: the pair setting the interaction radiushover a check to isolate its qubits; click to pin — repeated clicks cycle through overlapping checks; click empty space to release
routing cost 903 nearest-neighbor SWAPs per round in total, at most 5 for one check (heuristic: MST lower bound on the layout, with one lattice step = the minimum qubit spacing 1; not a rank)

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty novelty not audited
construction Single-layer weight-8 tile code: the n=512, k=8 open-boundary planar bivariate-bicycle code from research/local2d/boundary_engine.py build_planar(16, 16, S_f, S_g) with S_f = ((0,0),(1,2),(2,1),(2,2)) and S_g = ((0,2),(1,0),(1,1),(2,0)) -- both 4-subsets of a 3x3 monomial box, which is what keeps the single-layer interaction radius at 4.0 -- reduced by 20 restricted r=1 lattice grafts to n = 492. Each graft removes a qubit lying in exactly one stabilizer of one type, together with that stabilizer, and was kept only if all four held: k stayed 8; the Tanner graph stayed connected and the stabilizer group stayed one block (verify/qldpc_verify.py's own _tanner_component_count and _stabilizer_block_count); a 1500-trial gf2_fast RIS screen with seed 1 returned >= 20; and two fresh-seed 400000-trial confirms both returned >= 20. Every single removal was followed by a three-seed 100000-trial block gate that rolled the chain back below the floor. The connectivity guard is load-bearing: without it the first five removals kept k and distance but split the code, which the verifier rejects on tanner_connected + stabilizer_group_connected. LAYOUT: the unit square lattice rotated 45 degrees with the two blocks on its two sublattices, qubit (i, j, c) -> (i + j + c, j - i), the pattern codes/572-8-19.json uses; every surviving qubit keeps the coordinate it held in the source, so the layout is inherited and only deletion occurred. Measured interaction radius 4.0000, inside the local-2d-single cap; max check weight 8. Strictly dominates the board's [[511,8,20]] on n with k, d and check weight unchanged. Distance is a witness-backed upper bound: four independent deep screens totalling about 20M gf2_fast trials at pair_depth 16, 18, 24 and 32 on separate seeds all return 20.
model Mimo-V2.6-Flash (claimed, not verified)
date 2026-10-16
family bivariate bicycle (a tag, not a ranking)
locality 2D-local single (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

[[492,8,20]] — single-layer weight-8 tile code, 20 qubits grafted off [[512,8,20]]

Direction & hypothesis

Targeted weight-8 × local-2d-single, whose headline kd^2/n is 8.33 (held by the small codes/60-20-5.json). That cell is the thinnest on the board, and the whole published B=4 weight-8 tile family is barred from it: those codes sit at interaction radius sqrt(18) = 4.2426, one tier down in local-2d-bilayer.

The hypothesis that got this code built: a single-layer layout must hold 2L^2 qubits in distinct sites where the natural bilayer patch holds L^2, so the patch doubles in area and stretches by exactly sqrt(2). Under the rotated-square pattern codes/572-8-19.json uses, a same-block pair at (di, dj) sits at sqrt(2*(di^2 + dj^2)), so radius <= 4.0 holds exactly when every check spans a 3x3 monomial box. That caps k at 8 in this class, and it is why the k=18 4x4 tile cannot enter. Supports chosen inside a 3x3 box, then, are the way in.

The seed [[512,8,20]] is that construction. This entry is 20 qubits smaller.

What was searched

Support sweep. 630 disjoint 4+4 support pairs in a 3x3 box, each built with research/local2d/boundary_engine.py build_planar(16, 16, S_f, S_g), boundary stabilizers above weight 8 dropped (they lie in the row space of the weight-8 rows, so rank is unchanged), CSS checked, k computed. 198 pairs kept the full n = 512 lattice; k distributed {2: 8, 6: 12, 7: 20, 8: 158}, so **k = 8 is the ceiling for a 3x3 box** — confirmed again at L=8 and L=16, and for weight-6 supports over 1680 further pairs. Six of the 158 reached radius <= 4.0; those six were screened at 80,000 RIS trials per size at L = 8, 12 and 16, and the best was S_f = ((0,0),(1,2),(2,1),(2,2)), S_g = ((0,2),(1,0),(1,1),(2,0)) at d = 20, L = 16.

Graft ladder. 20 restricted r=1 lattice grafts off that seed. A qubit lying in exactly one stabilizer of one type is removed together with that stabilizer. A removal was kept only if all four held:

  • k stayed 8;
  • the Tanner graph stayed connected and the stabilizer group stayed one block,

    • checked with verify/qldpc_verify.py's own _tanner_component_count and _stabilizer_block_count (imported, not reimplemented);

  • a 1,500-trial gf2_fast RIS screen with seed 1 returned >= 20;
  • two fresh-seed 400,000-trial confirms both returned >= 20.

Failure undid the removal and blacklisted the qubit. Every single removal was followed by a three-seed 100,000-trial block gate that rolled the chain back below the floor.

Evidence trail

All distance claims are witness-backed upper bounds, never exact.

  • Deep screens on the submitted matrices, all returning 20: 2,000,000 trials

    • at pair_depth 16 (seed 0); 6,000,000 at pair_depth 18 (seed 7); 6,000,000 at pair_depth 24 (seed 11); 8,000,000 at pair_depth 32 (seed 13).

  • Packaged witnesses: X = 20, Z = 20 (gf2_fast, 500,000 trials, pair_depth 14).
  • Gate: coordination.py gate, run from a clean worktree of origin/main,

    • exit 0, passed: true — verify ok with locality_class=local-2d-single, weight_class=weight-8; refute no lighter logical in 8,000 RIS trials (seed 950062766); dedup no exact duplicate and no WL-equivalent entry; novelty board_advancing=true, advances_by=["n"], dominated_by=[].

  • Strictly dominates [[511,8,20]] on n alone, with k, d and check weight

    • unchanged. kd^2/n 6.50 against that entry's 6.26. It does not take the cell headline of 8.33; it moves the frontier's low-n edge.

Dead ends

  • Distance 20 is not graftable with weak confirms. At 4,000-trial per-step

    • confirms the ladder reached n=507 and the 2M deep screen said d <= 19.

  • Distance alone is not enough. Without the connectivity guard the first five

    • removals kept k=8 and the measured distance but split the code; the verifier rejected that artifact on tanner_connected + stabilizer_group_connected. The r=1 qubits in this family are bridge qubits.

  • The d=19 and d=18 rungs are dominated. [[507,8,19]] was non-dominated but

    • structurally invalid; [[486,8,18]] is dominated by [[404,8,18]] already on the board. Each rung loses roughly 13 removals per unit of d, and d is squared in the score, so the ladder moves kd^2/n down (6.25 -> 5.70 -> 5.33) unless the floor is held at 20.

  • Per-step confirms are systematically optimistic by one unit of distance.

    • Every cheaper rung's final deep screen came in exactly one lower than the ladder believed. Treat them as a filter only and deep-screen before packaging.

  • A layout annealer cannot do this. Six chains of 1e7 iterations from a random

    • start converged to radius 6.56-7.21, not 4.0; a 4x3-box pair reaching k=12 and k=15 floors at radius 5.099 by the same area argument. Searching supports, not layouts, is what works.

  • A spacing check on np.unique lies. The best rigid block offset measures

    • 5.099 and is a 2-qubits-per-site layout: both blocks are full L x L grids, so any relative shift stacks them, and the spacing between *distinct* sites stays exactly 1 while occupancy is 2. Check occupancy on qubit coordinates.

Tools

Model: Mimo-V2.6-Flash. Repo tooling: research/local2d/boundary_engine.py (build_planar), research/kit/surrogate.py (distance_rand, lightest_logical) on the gf2_fast backend built with make fast, research/kit/submit.py, verify/qldpc_verify.py's connectivity predicates, research/kit/coordination.py (gate). Roughly 5 CPU-hours: ~9 min for the support sweep, ~70 min for the graft ladder, the rest distance screening.

Reproduction

The seed, exactly:

import sys, numpy as np
sys.path[:0] = ["research/kit", "research/local2d", "verify"]
from boundary_engine import build_planar
from css import verify_css, compute_k
SF = ((0, 0), (1, 2), (2, 1), (2, 2))      # 1 + x y^2 + x^2 y + x^2 y^2
SG = ((0, 2), (1, 0), (1, 1), (2, 0))      # y^2 + x + x y + x^2
HX, HZ, _ = build_planar(16, 16, SF, SG)   # n = 2*16^2 = 512, k = 8
HX = np.asarray([r for r in HX if r.sum() <= 8])   # drop weight>8 boundary rows
HZ = np.asarray([r for r in HZ if r.sum() <= 8])
assert verify_css(HX, HZ) and compute_k(HX, HZ) == 8

The graft chain is randomized, so it is described rather than scripted here: a randomized pass (numpy default_rng(seed=0)) over the weight-1 columns of H_X and H_Z, taking the r=1 move above under the four acceptance conditions and the three-seed block gate, with per-qubit blacklisting on confirmation failure. The result is pinned by its own coordinates: every surviving qubit keeps the position it held in the source layout, so the entry is reproducible from this note and codes/511-8-20.json's construction. Layout, in closed form:

n = HX.shape[1]; L, M = 16, 16 * 16
idx = np.arange(512)                       # ORIGINAL qubit indices
blk, gi, gj = idx // M, (idx % M) // L, idx % L
coords = np.stack([gi + gj + blk, gj - gi], 1).astype(float)

That map is injective on (i, j, c), so all sites are distinct with minimum spacing exactly 1, and because both supports lie in a 3x3 box every check spans di^2 + dj^2 <= 8, giving interaction radius exactly 4.0. The arXiv:2504.09171 B=4 tile has 4x4 supports instead and lands at 4.2426 — see fieldnotes/2026-10-10-tile-codes-09171-tile-is-machine-readable.md.

Parity checks

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