{
 "schema_version": "0.2",
 "name": "[[90,24,6]] two-block code over C45",
 "code_type": "CSS",
 "n": 90,
 "k": 24,
 "checks": {
  "X": [
   [
    0,
    4,
    11,
    20,
    24,
    26,
    45,
    60,
    78
   ],
   [
    0,
    1,
    3,
    9,
    30,
    32,
    46,
    66,
    83
   ],
   [
    0,
    2,
    10,
    19,
    29,
    34,
    47,
    48,
    69
   ],
   [
    3,
    4,
    7,
    11,
    20,
    33,
    48,
    70,
    85
   ],
   [
    1,
    4,
    6,
    14,
    35,
    37,
    49,
    72,
    86
   ],
   [
    1,
    2,
    5,
    8,
    17,
    39,
    50,
    51,
    75
   ],
   [
    0,
    3,
    6,
    9,
    12,
    38,
    51,
    76,
    88
   ],
   [
    2,
    7,
    18,
    28,
    37,
    40,
    45,
    52,
    53
   ],
   [
    3,
    8,
    10,
    15,
    19,
    29,
    53,
    54,
    78
   ],
   [
    4,
    9,
    11,
    16,
    20,
    40,
    54,
    69,
    79
   ],
   [
    4,
    5,
    10,
    13,
    23,
    42,
    55,
    56,
    80
   ],
   [
    1,
    6,
    11,
    14,
    18,
    41,
    56,
    81,
    89
   ],
   [
    5,
    7,
    12,
    16,
    26,
    43,
    46,
    57,
    58
   ],
   [
    2,
    6,
    8,
    13,
    17,
    21,
    58,
    59,
    83
   ],
   [
    0,
    3,
    9,
    14,
    22,
    43,
    59,
    75,
    84
   ],
   [
    7,
    9,
    15,
    27,
    36,
    42,
    47,
    60,
    61
   ],
   [
    8,
    16,
    18,
    24,
    28,
    37,
    48,
    61,
    62
   ],
   [
    9,
    10,
    17,
    19,
    25,
    29,
    45,
    62,
    85
   ],
   [
    10,
    12,
    18,
    22,
    32,
    44,
    49,
    63,
    64
   ],
   [
    5,
    11,
    13,
    19,
    23,
    27,
    64,
    65,
    86
   ],
   [
    1,
    6,
    14,
    20,
    28,
    44,
    65,
    80,
    87
   ],
   [
    12,
    14,
    15,
    21,
    25,
    34,
    50,
    66,
    67
   ],
   [
    7,
    13,
    16,
    22,
    26,
    30,
    51,
    67,
    68
   ],
   [
    2,
    8,
    14,
    17,
    23,
    31,
    46,
    68,
    88
   ],
   [
    15,
    17,
    24,
    35,
    41,
    44,
    52,
    69,
    70
   ],
   [
    0,
    16,
    25,
    27,
    36,
    42,
    53,
    70,
    71
   ],
   [
    17,
    18,
    26,
    28,
    33,
    37,
    47,
    54,
    71
   ],
   [
    18,
    20,
    21,
    27,
    31,
    39,
    55,
    72,
    73
   ],
   [
    12,
    19,
    22,
    28,
    32,
    35,
    56,
    73,
    74
   ],
   [
    5,
    13,
    20,
    23,
    29,
    36,
    49,
    74,
    89
   ],
   [
    21,
    23,
    24,
    30,
    33,
    40,
    57,
    75,
    76
   ],
   [
    1,
    15,
    22,
    25,
    31,
    34,
    58,
    76,
    77
   ],
   [
    7,
    16,
    23,
    26,
    32,
    38,
    50,
    59,
    77
   ],
   [
    2,
    25,
    33,
    35,
    41,
    44,
    61,
    78,
    79
   ],
   [
    3,
    26,
    27,
    34,
    36,
    42,
    52,
    62,
    79
   ],
   [
    27,
    29,
    30,
    35,
    38,
    43,
    63,
    80,
    81
   ],
   [
    4,
    21,
    28,
    31,
    36,
    39,
    64,
    81,
    82
   ],
   [
    12,
    22,
    29,
    32,
    37,
    41,
    55,
    65,
    82
   ],
   [
    5,
    24,
    31,
    33,
    38,
    40,
    67,
    83,
    84
   ],
   [
    6,
    15,
    25,
    32,
    34,
    39,
    57,
    68,
    84
   ],
   [
    8,
    34,
    35,
    40,
    41,
    44,
    60,
    71,
    85
   ],
   [
    10,
    30,
    36,
    38,
    41,
    43,
    73,
    86,
    87
   ],
   [
    11,
    21,
    31,
    37,
    39,
    42,
    63,
    74,
    87
   ],
   [
    13,
    24,
    33,
    39,
    40,
    43,
    66,
    77,
    88
   ],
   [
    19,
    30,
    38,
    42,
    43,
    44,
    72,
    82,
    89
   ]
  ],
  "Z": [
   [
    0,
    7,
    17,
    45,
    46,
    47,
    51,
    59,
    70
   ],
   [
    1,
    12,
    23,
    46,
    49,
    50,
    56,
    65,
    76
   ],
   [
    2,
    15,
    26,
    47,
    50,
    52,
    58,
    68,
    78
   ],
   [
    2,
    3,
    16,
    46,
    48,
    51,
    53,
    59,
    79
   ],
   [
    4,
    18,
    29,
    45,
    48,
    49,
    54,
    55,
    81
   ],
   [
    5,
    21,
    32,
    50,
    55,
    57,
    64,
    74,
    83
   ],
   [
    5,
    6,
    22,
    49,
    51,
    56,
    58,
    65,
    84
   ],
   [
    7,
    24,
    34,
    48,
    52,
    57,
    60,
    67,
    77
   ],
   [
    7,
    8,
    25,
    50,
    53,
    58,
    61,
    68,
    85
   ],
   [
    8,
    9,
    26,
    46,
    51,
    54,
    59,
    60,
    62
   ],
   [
    10,
    27,
    37,
    47,
    53,
    55,
    62,
    63,
    86
   ],
   [
    10,
    11,
    28,
    45,
    48,
    54,
    56,
    64,
    87
   ],
   [
    12,
    30,
    39,
    51,
    57,
    63,
    66,
    73,
    82
   ],
   [
    12,
    13,
    31,
    55,
    58,
    64,
    67,
    74,
    88
   ],
   [
    13,
    14,
    32,
    49,
    56,
    59,
    65,
    66,
    68
   ],
   [
    0,
    15,
    40,
    53,
    60,
    66,
    69,
    76,
    84
   ],
   [
    15,
    16,
    33,
    54,
    57,
    61,
    67,
    70,
    77
   ],
   [
    16,
    17,
    34,
    50,
    58,
    62,
    68,
    69,
    71
   ],
   [
    18,
    35,
    42,
    52,
    56,
    61,
    63,
    71,
    72
   ],
   [
    18,
    19,
    36,
    47,
    53,
    62,
    64,
    73,
    89
   ],
   [
    19,
    20,
    37,
    45,
    48,
    54,
    65,
    72,
    74
   ],
   [
    1,
    21,
    43,
    58,
    66,
    72,
    75,
    81,
    87
   ],
   [
    21,
    22,
    38,
    59,
    63,
    67,
    73,
    76,
    82
   ],
   [
    22,
    23,
    39,
    55,
    64,
    68,
    74,
    75,
    77
   ],
   [
    2,
    9,
    24,
    45,
    61,
    69,
    75,
    83,
    88
   ],
   [
    3,
    24,
    25,
    62,
    66,
    70,
    76,
    78,
    84
   ],
   [
    25,
    26,
    40,
    45,
    57,
    67,
    71,
    77,
    79
   ],
   [
    4,
    27,
    44,
    60,
    64,
    70,
    72,
    79,
    80
   ],
   [
    27,
    28,
    41,
    52,
    61,
    65,
    71,
    73,
    81
   ],
   [
    28,
    29,
    42,
    47,
    53,
    62,
    74,
    80,
    82
   ],
   [
    5,
    14,
    30,
    46,
    67,
    75,
    80,
    86,
    89
   ],
   [
    6,
    30,
    31,
    68,
    72,
    76,
    81,
    83,
    87
   ],
   [
    31,
    32,
    43,
    46,
    63,
    73,
    77,
    82,
    84
   ],
   [
    0,
    8,
    33,
    48,
    71,
    75,
    78,
    83,
    88
   ],
   [
    9,
    33,
    34,
    47,
    66,
    76,
    79,
    84,
    85
   ],
   [
    10,
    20,
    35,
    49,
    69,
    73,
    78,
    80,
    85
   ],
   [
    11,
    35,
    36,
    60,
    70,
    74,
    79,
    81,
    86
   ],
   [
    36,
    37,
    44,
    49,
    52,
    61,
    71,
    82,
    87
   ],
   [
    1,
    13,
    38,
    51,
    77,
    80,
    83,
    86,
    89
   ],
   [
    14,
    38,
    39,
    50,
    72,
    81,
    84,
    87,
    88
   ],
   [
    3,
    17,
    40,
    52,
    54,
    75,
    83,
    85,
    88
   ],
   [
    4,
    19,
    41,
    56,
    69,
    78,
    82,
    85,
    86
   ],
   [
    20,
    41,
    42,
    55,
    60,
    70,
    79,
    87,
    89
   ],
   [
    6,
    23,
    43,
    57,
    59,
    80,
    86,
    88,
    89
   ],
   [
    11,
    29,
    44,
    63,
    65,
    69,
    78,
    85,
    89
   ]
  ]
 },
 "distance": {
  "d": 6,
  "X": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
    3,
    9,
    24,
    40,
    60,
    79
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1033
    ]
   }
  },
  "Z": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
    7,
    16,
    33,
    40,
    61,
    71
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1034
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C45 = SmallGroup(45, 1) (order 45), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 90; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 1, 2, 6, 14, 25}, b = {0, 7, 17} 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": "generalized-bicycle"
}
