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"generalized-bicycle", "provenance": { "authors": [ "@vprusso" ], "model": "Claude Opus 5", "novelty": "unknown", "origin": "submission", "date": "2026-10-15", "construction": "Cyclic generalized bicycle at m=257, a prime with ord_2(m)=16, so the nontrivial cyclotomic cosets of 2 all have size 16. The divisor g is one such coset's minimal polynomial, of degree 49, which fixes k = 2 deg g = 98 by construction. The pair (a,b) was then drawn from the ideal (g) by information-set decoding over sparse supports, keeping weights 12 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 = 514 qubits at uniform row weight 24, with a = [11, 17, 45, 62, 83, 94, 141, 178, 185, 193, 243, 250] and b = [20, 28, 62, 69, 86, 100, 106, 117, 155, 175, 191, 213].", "notes": "Distance is an upper bound from the lighter of two witnesses, weight 55 on X and 55 on Z, both carried in this file. A 24-seed randomized information-set search at 2,000,000 trials per seed spread 55 to 63 with the minimum found by one seed. A single run of 8,000,000 trials, matching the verifier's own depth, reads 61. A search restricted to logicals supported inside one circulant block, which a general search is blind to, found nothing below 69. Folding onto the x^t-invariant subspaces leaves a lightest surviving logical of weight 146. The design point is deg g / m = 0.191." } }