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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=223, a prime with ord_2(m)=37, so the nontrivial cyclotomic cosets of 2 all have size 37. The divisor g is one such coset's minimal polynomial, of degree 37, which fixes k = 2 deg g = 74 by construction. The pair (a,b) was then drawn from the ideal (g) by information-set decoding over sparse supports, keeping weights 9 and 11; 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 = 446 qubits at uniform row weight 20, with a = [26, 42, 110, 144, 178, 184, 196, 205, 211] and b = [9, 14, 24, 51, 67, 83, 85, 151, 168, 176, 180].", "notes": "Distance is an upper bound from the lighter of two witnesses, weight 50 on X and 50 on Z, both carried in this file. A 24-seed randomized information-set search at 2,000,000 trials per seed spread 50 to 54 with the minimum found by one seed. A single run of 8,000,000 trials, matching the verifier's own depth, reads 52. A search restricted to logicals supported inside one circulant block, which a general search is blind to, found nothing below 60. Folding onto the x^t-invariant subspaces leaves a lightest surviving logical of weight 142. The design point is deg g / m = 0.166." } }