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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=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 10 and 8; 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 18, with a = [9, 23, 32, 34, 36, 40, 105, 109, 215, 219] and b = [48, 70, 101, 149, 164, 177, 224, 229].",
  "notes": "Distance is an upper bound from the lighter of two witnesses, weight 56 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 56 to 60 with the minimum found by one seed. A single run of 8,000,000 trials, matching the verifier's own depth, reads 56. A search restricted to logicals supported inside one circulant block, which a general search is blind to, found nothing below 65. Folding onto the x^t-invariant subspaces leaves a lightest surviving logical of weight 176. The design point is deg g / m = 0.129."
 }
}