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 },
 "family": "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 the minimal polynomial of a cyclotomic coset of size 16, times x+1, of degree 17, which fixes k = 2 deg g = 34 by construction. The pair (a,b) was then drawn from the ideal (g) by information-set decoding over sparse supports, keeping weights 6 and 6. Both weights are even, so x+1 divides the gcd; m is prime, so the only block logical this forces has weight m and is far above the claim. H_X = [circ(a) | circ(b)] and H_Z = [circ(b)^T | circ(a)^T] on n = 2m = 514 qubits at uniform row weight 12, with a = [16, 35, 126, 179, 222, 254] and b = [39, 56, 132, 156, 208, 236].",
  "notes": "Distance is an upper bound from the lighter of two witnesses, weight 62 on X and 62 on Z, both carried in this file. A 24-seed randomized information-set search at 2,000,000 trials per seed spread 64 to 71, with the minimum reached by exactly one seed. A single run of 8,000,000 trials, matching the verifier's own depth, reads 65. 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 226. The design point is deg g / m = 0.066. Revised to 59 on 2026-10-17: a 2,000,000-trial information-set search found a weight-59 X logical against the claimed 62, and its block-swap mirror gives a Z logical of the same weight; both are carried here."
 }
}