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    215
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    182,
    193,
    211
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    22,
    82,
    86,
    111,
    175,
    183,
    194
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    10,
    87,
    95,
    112,
    176,
    184,
    195
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   [
    11,
    27,
    88,
    163,
    180,
    187,
    196
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   [
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    79,
    89,
    122,
    154,
    191,
    197
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   [
    24,
    57,
    90,
    136,
    182,
    196,
    198
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   [
    9,
    91,
    99,
    123,
    156,
    192,
    199
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   [
    26,
    54,
    92,
    114,
    124,
    137,
    200
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   [
    23,
    55,
    93,
    126,
    180,
    201,
    206
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   [
    35,
    69,
    94,
    160,
    188,
    195,
    202
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   [
    2,
    91,
    95,
    115,
    140,
    189,
    203
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   [
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    59,
    96,
    116,
    142,
    191,
    204
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   [
    4,
    20,
    97,
    146,
    176,
    194,
    205
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   [
    16,
    42,
    98,
    170,
    186,
    199,
    206
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   [
    38,
    43,
    99,
    119,
    131,
    200,
    207
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   [
    0,
    100,
    103,
    120,
    132,
    201,
    208
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   [
    28,
    48,
    101,
    123,
    197,
    204,
    209
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   [
    25,
    58,
    102,
    144,
    183,
    208,
    210
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   [
    10,
    51,
    103,
    128,
    145,
    163,
    211
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   [
    1,
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    129,
    147,
    165,
    212
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   [
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    41,
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    213
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   [
    3,
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    212,
    214
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   [
    7,
    29,
    107,
    153,
    173,
    190,
    215
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  ]
 },
 "distance": {
  "d": 20,
  "X": {
   "value": 20,
   "confidence": "upper_bound",
   "witness": [
    0,
    5,
    24,
    30,
    41,
    42,
    43,
    49,
    79,
    82,
    86,
    88,
    126,
    134,
    149,
    162,
    170,
    196,
    201,
    207
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1020
    ]
   }
  },
  "Z": {
   "value": 20,
   "confidence": "upper_bound",
   "witness": [
    5,
    10,
    51,
    52,
    64,
    69,
    71,
    95,
    112,
    131,
    148,
    161,
    163,
    172,
    177,
    178,
    183,
    188,
    189,
    201
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1021
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C12 x C3 x C3 = SmallGroup(108, 35) (order 108), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 216; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 23, 76, 106}, b = {0, 51, 86} 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": "generalized-bicycle"
}