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    153,
    155
   ],
   [
    33,
    46,
    73,
    75,
    109,
    110,
    134,
    138,
    156
   ],
   [
    20,
    51,
    64,
    76,
    114,
    115,
    121,
    125,
    157
   ],
   [
    9,
    74,
    77,
    80,
    116,
    122,
    126,
    158,
    159
   ],
   [
    10,
    23,
    54,
    78,
    117,
    124,
    128,
    157,
    159
   ],
   [
    28,
    59,
    77,
    79,
    122,
    123,
    129,
    147,
    160
   ],
   [
    24,
    41,
    68,
    80,
    135,
    136,
    142,
    144,
    161
   ]
  ]
 },
 "distance": {
  "d": 17,
  "X": {
   "value": 17,
   "confidence": "upper_bound",
   "witness": [
    6,
    13,
    22,
    23,
    42,
    59,
    69,
    73,
    79,
    101,
    108,
    110,
    112,
    117,
    140,
    150,
    152
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1018
    ]
   }
  },
  "Z": {
   "value": 17,
   "confidence": "upper_bound",
   "witness": [
    18,
    19,
    26,
    34,
    49,
    51,
    54,
    76,
    90,
    95,
    105,
    111,
    118,
    128,
    130,
    135,
    156
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1019
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C9 x C3 x C3 = SmallGroup(81, 11) (order 81), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 162; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 8, 24, 28, 80}, b = {0, 3, 21, 77} as element indices. Check weight 9. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race.",
  "references": [
   "arXiv:2610.13880"
  ],
  "date": "2026-10-12",
  "notes": "Parameters and construction taken from the public database of arXiv:2610.13880v1. Distance is an upper bound certified by the witnesses attached here. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race @ aed705a, CC BY 4.0; rebuilt here with the repo's own group data. Distance is an upper bound certified by the attached witnesses, not the paper's exact distance.",
  "origin": "baseline",
  "novelty": "known_parameters",
  "model": "Mimo-V2.6-Flash"
 },
 "family": "generalized-bicycle"
}