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   [
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    160,
    172,
    178,
    193
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   [
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    83,
    84,
    155,
    194,
    197,
    206
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    84,
    107,
    114,
    138,
    195,
    204
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   [
    78,
    80,
    85,
    163,
    175,
    181,
    196
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   [
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    43,
    86,
    158,
    197,
    200,
    209
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   [
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    82,
    87,
    117,
    141,
    198,
    207
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    45,
    88,
    166,
    178,
    184,
    199
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    33,
    89,
    161,
    200,
    203,
    212
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    41,
    90,
    120,
    144,
    201,
    210
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    29,
    91,
    169,
    181,
    187,
    202
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   [
    63,
    88,
    92,
    164,
    203,
    206,
    215
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   [
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    31,
    93,
    123,
    147,
    204,
    213
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   [
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    90,
    94,
    172,
    184,
    190,
    205
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   [
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    95,
    167,
    206,
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    96,
    126,
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    207,
    216
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   [
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    97,
    175,
    187,
    193,
    208
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   [
    12,
    22,
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    111,
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    91,
    99,
    129,
    153,
    210,
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   [
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    24,
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    196,
    211
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   [
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    101,
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    173,
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   [
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    132,
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   [
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    103,
    181,
    193,
    199,
    214
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    72,
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    176,
    215,
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   [
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    105,
    114,
    135,
    159,
    216
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    69,
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    184,
    196,
    202,
    217
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   [
    34,
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    111,
    119,
    179,
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   [
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   [
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    205,
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   [
    32,
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  ]
 },
 "distance": {
  "d": 21,
  "X": {
   "value": 21,
   "confidence": "upper_bound",
   "witness": [
    7,
    16,
    18,
    21,
    22,
    32,
    37,
    59,
    69,
    94,
    107,
    108,
    111,
    118,
    132,
    138,
    148,
    177,
    189,
    217,
    221
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1036
    ]
   }
  },
  "Z": {
   "value": 21,
   "confidence": "upper_bound",
   "witness": [
    7,
    10,
    25,
    28,
    31,
    37,
    43,
    46,
    67,
    70,
    76,
    82,
    85,
    97,
    109,
    145,
    153,
    177,
    187,
    194,
    212
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1037
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C37 : C3 = SmallGroup(111, 1) (order 111), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 222; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 2, 11, 71}, b = {0, 1, 21} as element indices. Check weight 7. 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": "2bga-nonabelian"
}