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 },
 "family": "generalized-bicycle",
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "model": "Claude Opus 5",
  "novelty": "unknown",
  "origin": "submission",
  "date": "2026-10-14",
  "construction": "Cyclic generalized bicycle at m=241, a prime with ord_2(m)=24, so the nontrivial cyclotomic cosets of 2 all have size 24. The divisor g is one such coset's minimal polynomial, of degree 24, which fixes k = 2 deg g = 48 by construction. The pair (a,b) was then drawn from the ideal (g) by information-set decoding over sparse supports, keeping weights 7 and 7; 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 = 482 qubits at uniform row weight 14, with a = [11, 45, 139, 186, 229, 234, 236] and b = [61, 70, 116, 126, 184, 200, 201].",
  "notes": "Distance is an upper bound from the lighter of two witnesses, weight 56 on X and 60 on Z, both carried in this file. A 24-seed randomized information-set search at 2,000,000 trials per seed spread 56 to 64 with the minimum found by one seed. A single run of 8,000,000 trials, matching the verifier's own depth, reads 62. A search restricted to logicals supported inside one circulant block, which a general search is blind to, found nothing below 72. Folding onto the x^t-invariant subspaces leaves a lightest surviving logical of weight 186. The design point is deg g / m = 0.100."
 }
}