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141, 143, 146, 152, 160, 172, 180, 278, 305, 310, 318, 320, 351, 354, 371, 384, 400, 404, 412, 433, 454 ], [ 32, 35, 70, 77, 80, 91, 103, 119, 138, 142, 144, 147, 153, 161, 173, 181, 279, 306, 311, 319, 321, 352, 355, 372, 385, 401, 405, 413, 434, 455 ] ] }, "family": "generalized-bicycle", "provenance": { "authors": [ "@vprusso" ], "model": "Claude Opus 5", "novelty": "unknown", "origin": "submission", "date": "2026-10-14", "construction": "Cyclic generalized bicycle at m=233, a prime with ord_2(m)=29, so the nontrivial cyclotomic cosets of 2 all have size 29. The divisor g is one such coset's minimal polynomial, of degree 59, which fixes k = 2 deg g = 118 by construction. The pair (a,b) was then drawn from the ideal (g) by information-set decoding over sparse supports, keeping weights 14 and 16; both are odd, so x+1 does not divide the gcd and no weight-m block logical is forced. H_X = [circ(a) | circ(b)] and H_Z = [circ(b)^T | circ(a)^T] on n = 2m = 466 qubits at uniform row weight 30, with a = [10, 31, 52, 60, 64, 80, 93, 110, 113, 144, 146, 154, 159, 186] and b = [51, 59, 71, 79, 85, 88, 90, 94, 113, 129, 141, 152, 155, 162, 197, 200].", "notes": "Distance is an upper bound from the lighter of two witnesses, weight 46 on X and 47 on Z, both carried in this file. A 24-seed randomized information-set search at 2,000,000 trials per seed spread 46 to 50 with the minimum found by one seed. A single run of 8,000,000 trials, matching the verifier's own depth, reads 48. A search restricted to logicals supported inside one circulant block, which a general search is blind to, found nothing below 50. Folding onto the x^t-invariant subspaces leaves a lightest surviving logical of weight 120. The design point is deg g / m = 0.253." } }