{
 "schema_version": "0.2",
 "name": "[[36,24,2]] two-block code over C3 x S3",
 "code_type": "CSS",
 "n": 36,
 "k": 24,
 "checks": {
  "X": [
   [
    0,
    3,
    8,
    9,
    14,
    17,
    18,
    21,
    26
   ],
   [
    1,
    5,
    6,
    11,
    12,
    16,
    19,
    23,
    29
   ],
   [
    1,
    2,
    5,
    7,
    11,
    13,
    20,
    25,
    31
   ],
   [
    0,
    3,
    8,
    9,
    14,
    17,
    18,
    21,
    26
   ],
   [
    0,
    3,
    4,
    8,
    10,
    15,
    22,
    28,
    33
   ],
   [
    1,
    5,
    6,
    11,
    12,
    16,
    19,
    23,
    29
   ],
   [
    4,
    6,
    10,
    12,
    15,
    16,
    24,
    30,
    34
   ],
   [
    1,
    2,
    5,
    7,
    11,
    13,
    20,
    25,
    31
   ],
   [
    0,
    3,
    8,
    9,
    14,
    17,
    18,
    21,
    26
   ],
   [
    2,
    7,
    9,
    13,
    14,
    17,
    27,
    32,
    35
   ],
   [
    0,
    3,
    4,
    8,
    10,
    15,
    22,
    28,
    33
   ],
   [
    1,
    5,
    6,
    11,
    12,
    16,
    19,
    23,
    29
   ],
   [
    4,
    6,
    10,
    12,
    15,
    16,
    24,
    30,
    34
   ],
   [
    1,
    2,
    5,
    7,
    11,
    13,
    20,
    25,
    31
   ],
   [
    2,
    7,
    9,
    13,
    14,
    17,
    27,
    32,
    35
   ],
   [
    0,
    3,
    4,
    8,
    10,
    15,
    22,
    28,
    33
   ],
   [
    4,
    6,
    10,
    12,
    15,
    16,
    24,
    30,
    34
   ],
   [
    2,
    7,
    9,
    13,
    14,
    17,
    27,
    32,
    35
   ]
  ],
  "Z": [
   [
    0,
    3,
    8,
    18,
    21,
    22,
    26,
    28,
    33
   ],
   [
    1,
    5,
    11,
    19,
    20,
    23,
    25,
    29,
    31
   ],
   [
    2,
    7,
    13,
    20,
    25,
    27,
    31,
    32,
    35
   ],
   [
    0,
    3,
    8,
    18,
    21,
    22,
    26,
    28,
    33
   ],
   [
    4,
    10,
    15,
    22,
    24,
    28,
    30,
    33,
    34
   ],
   [
    1,
    5,
    11,
    19,
    20,
    23,
    25,
    29,
    31
   ],
   [
    6,
    12,
    16,
    19,
    23,
    24,
    29,
    30,
    34
   ],
   [
    2,
    7,
    13,
    20,
    25,
    27,
    31,
    32,
    35
   ],
   [
    0,
    3,
    8,
    18,
    21,
    22,
    26,
    28,
    33
   ],
   [
    9,
    14,
    17,
    18,
    21,
    26,
    27,
    32,
    35
   ],
   [
    4,
    10,
    15,
    22,
    24,
    28,
    30,
    33,
    34
   ],
   [
    1,
    5,
    11,
    19,
    20,
    23,
    25,
    29,
    31
   ],
   [
    6,
    12,
    16,
    19,
    23,
    24,
    29,
    30,
    34
   ],
   [
    2,
    7,
    13,
    20,
    25,
    27,
    31,
    32,
    35
   ],
   [
    9,
    14,
    17,
    18,
    21,
    26,
    27,
    32,
    35
   ],
   [
    4,
    10,
    15,
    22,
    24,
    28,
    30,
    33,
    34
   ],
   [
    6,
    12,
    16,
    19,
    23,
    24,
    29,
    30,
    34
   ],
   [
    9,
    14,
    17,
    18,
    21,
    26,
    27,
    32,
    35
   ]
  ]
 },
 "distance": {
  "d": 2,
  "X": {
   "value": 2,
   "confidence": "upper_bound",
   "witness": [
    22,
    28
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1043
    ]
   }
  },
  "Z": {
   "value": 2,
   "confidence": "upper_bound",
   "witness": [
    18,
    21
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1044
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C3 x S3 = SmallGroup(18, 3) (order 18), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 36; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 3, 4, 8, 10, 15}, b = {0, 3, 8} 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": "2bga-nonabelian"
}