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    155,
    156
   ],
   [
    28,
    50,
    55,
    76,
    81,
    95,
    112,
    156,
    159
   ],
   [
    54,
    56,
    76,
    77,
    97,
    103,
    116,
    122,
    157
   ],
   [
    58,
    62,
    77,
    78,
    83,
    107,
    117,
    120,
    158
   ],
   [
    44,
    65,
    69,
    79,
    87,
    110,
    115,
    128,
    159
   ]
  ]
 },
 "distance": {
  "d": 16,
  "X": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": [
    2,
    10,
    12,
    20,
    24,
    26,
    38,
    42,
    90,
    101,
    106,
    108,
    119,
    126,
    143,
    155
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1010
    ]
   }
  },
  "Z": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": [
    1,
    5,
    53,
    58,
    70,
    73,
    85,
    88,
    91,
    92,
    101,
    114,
    118,
    136,
    139,
    154
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1011
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C40 x C2 = SmallGroup(80, 23) (order 80), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 160; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 3, 41, 60, 65}, b = {0, 6, 56, 73} 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"
}