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 "distance": {
  "d": 32,
  "X": {
   "value": 32,
   "confidence": "upper_bound",
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    "found_by": [
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    "date": "2026-10-15",
    "found_at_samples": 400,
    "survived_samples": 400,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
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    "date": "2026-10-15",
    "found_at_samples": 400,
    "survived_samples": 400,
    "tool": "research/kit/surrogate.lightest_logical",
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 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "construction": "Cyclic generalized bicycle at m=171 = 3 x 3 x 19, with ord_2(m)=18, so x^171 - 1 factors over GF(2) into 12 cyclotomic cosets, 1 of size 1, 1 of size 2, 1 of size 6, 9 of size 18. The divisor g is assembled from coset minimal polynomials to degree 20, which fixes k = 2 deg g = 40 by construction, and (a,b) was drawn from the ideal (g) by information-set decoding over sparse supports, keeping weight 5 and weight 9 in the two blocks. At least one weight is odd, so x+1 does not divide the gcd. m is composite, so the quotient fold acts at t=3, t=9, t=19 and t=57; a fold over every equal-orbit partition of the qubits returns nothing lighter than 48, clear of the claim. H_X = [circ(a) | circ(b)] and H_Z = [circ(b)^T | circ(a)^T] on n = 2m = 342 qubits at uniform row weight 14, with a = [67, 71, 118, 165, 169] and b = [13, 14, 15, 49, 58, 79, 97, 132, 159].",
  "references": [],
  "date": "2026-10-15",
  "notes": "",
  "model": "Claude Opus 5"
 },
 "family": "generalized-bicycle"
}