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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=127, a prime with ord_2(m)=7, so the nontrivial cyclotomic cosets of 2 all have size 7. The divisor g is a product of the minimal polynomials of 9 cyclotomic cosets of size 7, of degree 63, which fixes k = 2 deg g = 126 by construction. The pair (a,b) was then drawn from the ideal (g) by information-set decoding over sparse supports, keeping weights 15 and 15. At least one weight is odd, so x+1 does not divide the gcd. H_X = [circ(a) | circ(b)] and H_Z = [circ(b)^T | circ(a)^T] on n = 2m = 254 qubits at uniform row weight 30, with a = [23, 27, 31, 32, 38, 51, 54, 55, 61, 79, 81, 93, 113, 114, 120] and b = [4, 7, 9, 21, 30, 34, 47, 58, 66, 67, 73, 76, 89, 111, 114].",
  "notes": "Distance is an upper bound from the lighter of two witnesses, weight 14 on X and 14 on Z, both carried in this file. A 24-seed randomized information-set search at 2,000,000 trials per seed read 14 on every seed. A single run of 8,000,000 trials, matching the verifier's own depth, reads 14. A search restricted to logicals supported inside one circulant block, which a general search is blind to, found nothing below 14. Folding onto the x^t-invariant subspaces leaves a lightest surviving logical of weight 30. The design point is deg g / m = 0.496."
 }
}