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401, 439 ], [ 4, 36, 64, 108, 123, 144, 150, 159, 196, 213, 216, 222, 238, 273, 286, 301, 340, 348, 402, 440 ] ] }, "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 30, which fixes k = 2 deg g = 60 by construction. The pair (a,b) was then drawn from the ideal (g) by information-set decoding over sparse supports, keeping weights 8 and 12; 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 20, with a = [25, 63, 117, 125, 164, 179, 192, 227] and b = [10, 16, 19, 36, 73, 82, 88, 109, 124, 168, 196, 228].", "notes": "Distance is an upper bound from the lighter of two witnesses, weight 57 on X and 57 on Z, both carried in this file. A 24-seed randomized information-set search at 2,000,000 trials per seed spread 57 to 61 with the minimum found by one seed. A single run of 8,000,000 trials, matching the verifier's own depth, reads 58. A search restricted to logicals supported inside one circulant block, which a general search is blind to, found nothing below 68. Folding onto the x^t-invariant subspaces leaves a lightest surviving logical of weight 176. The design point is deg g / m = 0.129." } }