{ "schema_version": "0.2", "name": "[[482,146,36]] prime-index cyclic generalized-bicycle code on Z_241", "code_type": "CSS", "n": 482, "k": 146, "checks": { "X": [ [ 0, 5, 14, 22, 31, 41, 78, 108, 145, 155, 164, 172, 181, 186, 241, 242, 250, 251, 281, 292, 319, 335, 358, 375, 398, 414, 441, 452 ], [ 1, 6, 15, 23, 32, 42, 79, 109, 146, 156, 165, 173, 182, 187, 242, 243, 251, 252, 282, 293, 320, 336, 359, 376, 399, 415, 442, 453 ], [ 2, 7, 16, 24, 33, 43, 80, 110, 147, 157, 166, 174, 183, 188, 243, 244, 252, 253, 283, 294, 321, 337, 360, 377, 400, 416, 443, 454 ], [ 3, 8, 17, 25, 34, 44, 81, 111, 148, 158, 167, 175, 184, 189, 244, 245, 253, 254, 284, 295, 322, 338, 361, 378, 401, 417, 444, 455 ], [ 4, 9, 18, 26, 35, 45, 82, 112, 149, 159, 168, 176, 185, 190, 245, 246, 254, 255, 285, 296, 323, 339, 362, 379, 402, 418, 445, 456 ], [ 5, 10, 19, 27, 36, 46, 83, 113, 150, 160, 169, 177, 186, 191, 246, 247, 255, 256, 286, 297, 324, 340, 363, 380, 403, 419, 446, 457 ], [ 6, 11, 20, 28, 37, 47, 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(GPU RIS, CPU re-verified)", "seeds": [ 4102 ] } }, "Z": { "value": 36, "confidence": "upper_bound", "witness": [ 5, 6, 12, 14, 19, 29, 32, 35, 36, 43, 44, 50, 65, 84, 88, 107, 122, 128, 129, 136, 137, 140, 143, 153, 158, 160, 166, 167, 175, 238, 331, 353, 357, 362, 366, 388 ], "witness_provenance": { "found_by": [ "@FarLab" ], "date": "2026-08-19", "found_at_samples": 1000000000, "tool": "ris_gpu", "seeds": [ 88000007 ] } } }, "family": "generalized-bicycle", "provenance": { "authors": [ "@yhu1996" ], "origin": "submission", "construction": "Generalized bicycle (two-block cyclic) code on Z_241 with m=241 PRIME. H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] on n = 2m = 482 qubits. a and b are low-weight codewords of a cyclic divisor ideal , g | x^241 - 1, where g is assembled in one step as a product over a chosen union of 2-cyclotomic cosets of Z_241 of total degree 72. This fixes k = 2 deg gcd(a, b, x^241 - 1) = 146 by design before any distance search, giving rate 0.303. a exponents = [0, 5, 14, 22, 31, 41, 78, 108, 145, 155, 164, 172, 181, 186] (weight 14); b exponents = [0, 1, 9, 10, 40, 51, 78, 94, 117, 134, 157, 173, 200, 211] (weight 14); max check weight 28. Design rationale: choosing m PRIME empties the shift-invariant (period) and coset-union subspaces of Z_m, because Z_m then has no proper nontrivial subgroup. On composite m those subspaces are where two-block cyclic codes carry their lightest logicals -- e.g. on a sibling code at m = 273 = 3*7*13 the period sector at t = 3 cut the honest distance from 48 to 36. Both a and b are mined light codewords of rather than random multiples of g (random multiples give d = 4-7), and a == b draws are rejected since (u,u) is then automatically a logical and forces d = 2.", "model": "Claude Opus 5", "references": [ "arXiv:2308.07915", "arXiv:2306.16400" ], "date": "2026-08-07", "notes": "Found by Jukebox-Autoresearch. Distance is a witness-backed UPPER bound (d <= 42), not exact. The bound was tightened from an initially staged 45 in three stages: (i) a Lee-Brickell search restricted to the four active 2-cyclotomic component subspaces (k = 146 = 2 + 3*48; 392 searches, ~4.1M subspace trials) found nothing below 44; (ii) Lee-Brickell on the full 314-dimensional kernel (60 runs) likewise found nothing below 44; (iii) witness-returning RIS run of 128M total trials (2M trials per configuration over 8 seeds x pair-depths {8,16,24,32} x both orientations) exhibited the weight-42 X-logical packaged here (seed 123457, pair_depth 24). No independent-mechanism cross-check was completed: the pinned BP+OSD decoder (decode/distance.py) exceeded the available budget at this size, so the corroboration is linear-algebraic only. Novelty vs the literature is UNVERIFIED; the construction is a generalized bicycle code, a well-mined family, and while no board entry has these parameters we have not searched the literature for an equivalent [[482,146]] code. No equivalence to an existing board entry is known: the gate reported no exact duplicate and no Weisfeiler-Leman-equivalent entry. Distance revised 2026-08-19 by GPU deep refutation with the board's standalone ris_gpu tool (verify/ris_gpu.cu, sqetch kernels by Muzhou Ma, MIT) on an NVIDIA L40S: a 1,000,000,000-trial random-ISD recovery ladder per side (seed 88000007) committed a weight-36 Z logical, re-verified on the CPU with the repo's GF(2) arithmetic and recorded here as the new Z witness. The same budget found no X logical lighter than weight 43, so the claimed dX<=42 stands. This tightens d<=42 to d<=36 and the score from 146*42^2/482 = 534.26 to 146*36^2/482 = 392.55. The distance remains a witness-backed upper bound, not an exact-distance claim. @yhu1996 constructed the code. Refutation credit and the search budget are recorded in witness_provenance on each corrected side (schema 0.2, issue #611); authorship is unchanged." } }