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   ],
   [
    16,
    41,
    107,
    131,
    179,
    219
   ],
   [
    10,
    76,
    108,
    129,
    220,
    223
   ],
   [
    11,
    47,
    109,
    135,
    150,
    221
   ],
   [
    9,
    50,
    110,
    139,
    154,
    222
   ],
   [
    0,
    24,
    111,
    144,
    147,
    223
   ]
  ]
 },
 "distance": {
  "d": 16,
  "X": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": [
    15,
    18,
    22,
    27,
    56,
    70,
    92,
    107,
    151,
    166,
    179,
    181,
    182,
    192,
    197,
    211
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1021
    ]
   }
  },
  "Z": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": [
    6,
    33,
    43,
    49,
    66,
    82,
    88,
    98,
    108,
    142,
    145,
    147,
    150,
    155,
    198,
    210
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1022
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C7 x QD16 = SmallGroup(112, 25) (order 112), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 224; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 3, 45}, b = {0, 17, 36} 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"
}