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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=151, a prime with ord_2(m)=15, so the nontrivial cyclotomic cosets of 2 all have size 15. The divisor g is a product of the minimal polynomials of 4 cyclotomic cosets of size 15, of degree 60, which fixes k = 2 deg g = 120 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 = 302 qubits at uniform row weight 30, with a = [1, 14, 19, 21, 38, 42, 48, 55, 57, 61, 65, 79, 85, 121, 150] and b = [4, 7, 12, 50, 66, 75, 82, 83, 90, 103, 118, 121, 128, 142, 145].",
  "notes": "Distance is an upper bound from the lighter of two witnesses, weight 20 on X and 20 on Z, both carried in this file. A 24-seed randomized information-set search at 2,000,000 trials per seed read 20 on every seed. A single run of 8,000,000 trials, matching the verifier's own depth, reads 20. A search restricted to logicals supported inside one circulant block, which a general search is blind to, found nothing below 20. Folding onto the x^t-invariant subspaces leaves a lightest surviving logical of weight 48. The design point is deg g / m = 0.397."
 }
}