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    255,
    282,
    325
   ],
   [
    25,
    44,
    161,
    166,
    183,
    256,
    283,
    326
   ],
   [
    26,
    45,
    162,
    167,
    184,
    257,
    284,
    327
   ],
   [
    27,
    46,
    163,
    168,
    185,
    258,
    285,
    328
   ],
   [
    28,
    47,
    164,
    169,
    186,
    259,
    286,
    329
   ],
   [
    29,
    48,
    165,
    170,
    187,
    260,
    287,
    330
   ],
   [
    30,
    49,
    166,
    171,
    188,
    261,
    288,
    331
   ],
   [
    31,
    50,
    167,
    172,
    189,
    262,
    289,
    332
   ],
   [
    32,
    51,
    168,
    173,
    190,
    263,
    290,
    333
   ],
   [
    33,
    52,
    169,
    174,
    191,
    264,
    291,
    334
   ]
  ]
 },
 "distance": {
  "d": 31,
  "X": {
   "value": 31,
   "confidence": "upper_bound",
   "witness": [
    6,
    10,
    25,
    29,
    66,
    71,
    81,
    86,
    91,
    100,
    149,
    168,
    173,
    180,
    183,
    188,
    191,
    215,
    222,
    226,
    261,
    269,
    285,
    291,
    295,
    312,
    323,
    330,
    339,
    344,
    349
   ]
  },
  "Z": {
   "value": 31,
   "confidence": "upper_bound",
   "witness": [
    7,
    12,
    17,
    26,
    33,
    44,
    61,
    65,
    71,
    87,
    95,
    130,
    134,
    141,
    165,
    168,
    173,
    176,
    183,
    188,
    207,
    256,
    265,
    270,
    275,
    285,
    290,
    327,
    331,
    346,
    350
   ]
  }
 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "construction": "Cyclic generalized-bicycle code on the ring x^178 - 1 with a(x) = x^21 + x^64 + x^91 + x^164, b(x) = x^3 + x^8 + x^125 + x^144; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].",
  "origin": "submission",
  "novelty": "known_parameters",
  "model": "Claude Opus 5",
  "date": "2026-09-21",
  "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"
}