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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=341, a prime with ord_2(m)=10, so the nontrivial cyclotomic cosets of 2 all have size 10. The divisor g is one such coset's minimal polynomial, of degree 20, which fixes k = 2 deg g = 40 by construction. The pair (a,b) was then drawn from the ideal (g) by information-set decoding over sparse supports, keeping weights 5 and 5; 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 = 682 qubits at uniform row weight 10, with a = [2, 197, 231, 232, 271] and b = [49, 215, 253, 290, 292].",
  "notes": "Distance is an upper bound from the lighter of two witnesses, weight 66 on X and 66 on Z, both carried in this file. A 24-seed randomized information-set search at 2,000,000 trials per seed spread 80 to 92 with the minimum found by one seed. A single run of 8,000,000 trials, matching the verifier's own depth, reads 88. A search restricted to logicals supported inside one circulant block, which a general search is blind to, found nothing below 100. The claim itself comes from folding onto the x^t-invariant subspaces: a weight-66 logical there, validated against both check matrices, which is why each randomised search above reads higher than the claim rather than confirming it. The design point is deg g / m = 0.059."
 }
}
