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    92,
    93,
    95,
    172
   ],
   [
    16,
    23,
    48,
    84,
    93,
    94,
    96,
    173
   ],
   [
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    24,
    49,
    85,
    94,
    95,
    97,
    174
   ],
   [
    18,
    25,
    50,
    86,
    95,
    96,
    98,
    175
   ],
   [
    19,
    26,
    51,
    87,
    96,
    97,
    99,
    176
   ],
   [
    20,
    27,
    52,
    88,
    97,
    98,
    100,
    177
   ]
  ]
 },
 "distance": {
  "d": 13,
  "X": {
   "value": 13,
   "confidence": "upper_bound",
   "witness": [
    3,
    21,
    46,
    49,
    53,
    56,
    71,
    85,
    136,
    138,
    139,
    142,
    145
   ]
  },
  "Z": {
   "value": 13,
   "confidence": "upper_bound",
   "witness": [
    22,
    25,
    28,
    29,
    31,
    96,
    111,
    114,
    118,
    121,
    146,
    164,
    171
   ]
  }
 },
 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "Univariate bicycle code over R_89 = F2[x]/(x^89-1); a(x) = 1 + x^9 + x^10 + x^12; b(x) = a(x^(2^5)) mod (x^89-1) (Frobenius coupling, gcd(89,32)=1 so wt(b)=wt(a)); H_X=[A,B], H_Z=[B^T,A^T]. Reconstruction of arXiv:2605.14173v1 Table I row 3.",
  "origin": "submission",
  "date": "2026-08-23",
  "model": "Ox Alpha 1.0"
 },
 "family": "generalized-bicycle"
}