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    236
   ],
   [
    12,
    99,
    100,
    190,
    219,
    238
   ],
   [
    31,
    52,
    100,
    146,
    191,
    220
   ],
   [
    3,
    73,
    101,
    147,
    221,
    237
   ],
   [
    1,
    102,
    103,
    163,
    172,
    222
   ],
   [
    24,
    103,
    119,
    173,
    209,
    223
   ],
   [
    43,
    104,
    105,
    165,
    224,
    230
   ],
   [
    38,
    89,
    105,
    211,
    225,
    231
   ],
   [
    6,
    45,
    106,
    167,
    226,
    232
   ],
   [
    20,
    107,
    108,
    178,
    204,
    227
   ],
   [
    42,
    64,
    108,
    179,
    228,
    234
   ],
   [
    7,
    84,
    109,
    206,
    229,
    233
   ],
   [
    5,
    110,
    111,
    207,
    230,
    233
   ],
   [
    35,
    48,
    111,
    133,
    208,
    231
   ],
   [
    10,
    55,
    112,
    134,
    232,
    239
   ],
   [
    13,
    30,
    113,
    168,
    213,
    233
   ],
   [
    9,
    114,
    115,
    187,
    196,
    234
   ],
   [
    46,
    60,
    115,
    197,
    227,
    235
   ],
   [
    18,
    67,
    116,
    189,
    236,
    238
   ],
   [
    21,
    41,
    117,
    202,
    223,
    237
   ],
   [
    17,
    26,
    118,
    151,
    226,
    238
   ],
   [
    25,
    37,
    119,
    210,
    218,
    239
   ]
  ]
 },
 "distance": {
  "d": 14,
  "X": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    8,
    23,
    67,
    68,
    69,
    84,
    88,
    100,
    109,
    128,
    151,
    191,
    203,
    238
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1025
    ]
   }
  },
  "Z": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    27,
    60,
    96,
    108,
    131,
    132,
    152,
    172,
    173,
    177,
    192,
    216,
    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": [
     1026
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C3 x ((C10 x C2) : C2) = SmallGroup(120, 20) (order 120), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 240; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 7, 12}, b = {0, 16, 96} as element indices. Check weight 6. 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"
}