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 "distance": {
  "d": 30,
  "X": {
   "value": 30,
   "confidence": "upper_bound",
   "witness": [
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  "Z": {
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   "confidence": "upper_bound",
   "witness": [
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 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "construction": "Cyclic generalized-bicycle code on the ring x^165 - 1 with a(x) = x^16 + x^23 + x^58 + x^59 + x^86 + x^129 + x^134 + x^149 + x^154 + x^161 + x^164, b(x) = x^11 + x^15 + x^18 + x^19 + x^45 + x^60 + x^67 + x^90 + x^133 + x^138 + x^153 + x^157 + x^163; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].",
  "origin": "submission",
  "novelty": "known_parameters",
  "model": "Claude Opus 5",
  "date": "2026-09-24",
  "notes": "Found by a randomized sweep over sparse polynomial pairs, screened against the live board before any expensive work. Checked for single-block logicals via the ideal generated by (x^m - 1)/gcd(a, x^m - 1) before the distance was believed."
 },
 "family": "generalized-bicycle"
}