{
 "schema_version": "0.2",
 "name": "[[120,12,14]] two-block code over C30 x C2",
 "code_type": "CSS",
 "n": 120,
 "k": 12,
 "checks": {
  "X": [
   [
    0,
    18,
    33,
    55,
    60,
    90,
    95,
    116
   ],
   [
    1,
    24,
    39,
    52,
    61,
    96,
    101,
    113
   ],
   [
    2,
    10,
    42,
    50,
    62,
    81,
    104,
    111
   ],
   [
    2,
    3,
    12,
    38,
    63,
    69,
    106,
    119
   ],
   [
    4,
    30,
    45,
    59,
    60,
    64,
    73,
    102
   ],
   [
    5,
    15,
    45,
    47,
    65,
    87,
    106,
    109
   ],
   [
    5,
    6,
    17,
    32,
    66,
    74,
    111,
    118
   ],
   [
    7,
    36,
    50,
    58,
    61,
    67,
    68,
    107
   ],
   [
    0,
    8,
    20,
    29,
    64,
    68,
    113,
    117
   ],
   [
    9,
    21,
    52,
    57,
    62,
    66,
    69,
    93
   ],
   [
    8,
    10,
    22,
    48,
    70,
    79,
    109,
    114
   ],
   [
    9,
    11,
    23,
    49,
    63,
    71,
    80,
    84
   ],
   [
    12,
    24,
    42,
    54,
    64,
    72,
    85,
    112
   ],
   [
    1,
    13,
    23,
    26,
    67,
    73,
    114,
    116
   ],
   [
    14,
    27,
    54,
    55,
    63,
    65,
    74,
    99
   ],
   [
    13,
    15,
    28,
    43,
    75,
    85,
    104,
    117
   ],
   [
    14,
    16,
    29,
    44,
    66,
    76,
    78,
    86
   ],
   [
    17,
    18,
    47,
    57,
    67,
    77,
    79,
    115
   ],
   [
    3,
    18,
    31,
    40,
    71,
    78,
    101,
    118
   ],
   [
    4,
    19,
    32,
    41,
    68,
    72,
    75,
    79
   ],
   [
    15,
    20,
    33,
    58,
    69,
    76,
    80,
    105
   ],
   [
    19,
    21,
    34,
    56,
    65,
    70,
    81,
    91
   ],
   [
    5,
    20,
    22,
    35,
    71,
    82,
    92,
    96
   ],
   [
    10,
    23,
    36,
    52,
    72,
    83,
    97,
    118
   ],
   [
    6,
    24,
    34,
    37,
    76,
    84,
    95,
    119
   ],
   [
    7,
    25,
    35,
    38,
    70,
    73,
    77,
    85
   ],
   [
    10,
    26,
    39,
    59,
    71,
    74,
    86,
    110
   ],
   [
    25,
    27,
    40,
    53,
    62,
    75,
    87,
    97
   ],
   [
    2,
    26,
    28,
    41,
    76,
    88,
    90,
    98
   ],
   [
    15,
    29,
    30,
    55,
    77,
    89,
    91,
    119
   ],
   [
    11,
    30,
    43,
    51,
    61,
    78,
    82,
    90
   ],
   [
    1,
    12,
    31,
    44,
    79,
    83,
    87,
    91
   ],
   [
    18,
    27,
    32,
    45,
    80,
    88,
    92,
    114
   ],
   [
    13,
    31,
    33,
    46,
    74,
    81,
    93,
    103
   ],
   [
    0,
    14,
    32,
    34,
    82,
    94,
    104,
    107
   ],
   [
    21,
    35,
    47,
    58,
    78,
    83,
    95,
    108
   ],
   [
    16,
    36,
    46,
    48,
    60,
    84,
    88,
    96
   ],
   [
    0,
    17,
    37,
    49,
    81,
    85,
    89,
    97
   ],
   [
    21,
    24,
    38,
    50,
    82,
    86,
    98,
    117
   ],
   [
    8,
    37,
    39,
    51,
    69,
    87,
    99,
    108
   ],
   [
    1,
    9,
    38,
    40,
    88,
    100,
    102,
    109
   ],
   [
    27,
    41,
    42,
    59,
    84,
    89,
    101,
    103
   ],
   [
    6,
    22,
    42,
    53,
    67,
    90,
    94,
    102
   ],
   [
    2,
    7,
    23,
    43,
    91,
    95,
    99,
    103
   ],
   [
    30,
    39,
    44,
    54,
    70,
    92,
    100,
    104
   ],
   [
    3,
    25,
    43,
    45,
    86,
    93,
    105,
    113
   ],
   [
    4,
    26,
    44,
    46,
    62,
    94,
    106,
    115
   ],
   [
    3,
    28,
    47,
    56,
    64,
    96,
    100,
    107
   ],
   [
    4,
    5,
    29,
    48,
    93,
    97,
    101,
    108
   ],
   [
    33,
    36,
    49,
    57,
    75,
    94,
    98,
    109
   ],
   [
    6,
    19,
    48,
    50,
    80,
    99,
    110,
    116
   ],
   [
    7,
    20,
    49,
    51,
    65,
    100,
    111,
    112
   ],
   [
    8,
    16,
    34,
    52,
    77,
    102,
    106,
    112
   ],
   [
    9,
    17,
    35,
    53,
    60,
    103,
    110,
    113
   ],
   [
    11,
    37,
    53,
    54,
    68,
    98,
    105,
    114
   ],
   [
    11,
    13,
    40,
    55,
    72,
    107,
    111,
    115
   ],
   [
    12,
    14,
    41,
    56,
    61,
    105,
    108,
    116
   ],
   [
    16,
    31,
    56,
    57,
    73,
    92,
    110,
    117
   ],
   [
    19,
    28,
    46,
    58,
    63,
    89,
    112,
    118
   ],
   [
    22,
    25,
    51,
    59,
    66,
    83,
    115,
    119
   ]
  ],
  "Z": [
   [
    0,
    4,
    36,
    53,
    60,
    68,
    94,
    97
   ],
   [
    1,
    7,
    30,
    56,
    61,
    73,
    91,
    100
   ],
   [
    2,
    9,
    27,
    46,
    62,
    63,
    88,
    103
   ],
   [
    3,
    11,
    14,
    58,
    63,
    78,
    105,
    107
   ],
   [
    4,
    8,
    12,
    47,
    64,
    79,
    106,
    108
   ],
   [
    5,
    14,
    21,
    51,
    65,
    66,
    82,
    108
   ],
   [
    6,
    9,
    16,
    59,
    66,
    84,
    102,
    110
   ],
   [
    7,
    13,
    17,
    42,
    67,
    85,
    103,
    111
   ],
   [
    7,
    8,
    19,
    54,
    68,
    70,
    99,
    112
   ],
   [
    3,
    9,
    20,
    39,
    69,
    71,
    100,
    113
   ],
   [
    10,
    21,
    25,
    44,
    62,
    70,
    83,
    86
   ],
   [
    11,
    18,
    22,
    26,
    71,
    90,
    114,
    115
   ],
   [
    12,
    19,
    23,
    55,
    63,
    72,
    91,
    116
   ],
   [
    4,
    13,
    25,
    57,
    73,
    75,
    93,
    115
   ],
   [
    6,
    14,
    26,
    33,
    74,
    76,
    94,
    116
   ],
   [
    15,
    19,
    27,
    49,
    65,
    75,
    80,
    89
   ],
   [
    16,
    20,
    24,
    28,
    76,
    96,
    112,
    117
   ],
   [
    17,
    25,
    29,
    52,
    66,
    77,
    97,
    113
   ],
   [
    16,
    18,
    30,
    35,
    60,
    77,
    78,
    92
   ],
   [
    10,
    17,
    19,
    31,
    79,
    81,
    110,
    118
   ],
   [
    11,
    20,
    32,
    50,
    68,
    80,
    82,
    111
   ],
   [
    2,
    21,
    33,
    37,
    69,
    81,
    95,
    98
   ],
   [
    22,
    30,
    34,
    38,
    70,
    82,
    102,
    119
   ],
   [
    23,
    31,
    35,
    59,
    71,
    73,
    83,
    103
   ],
   [
    11,
    24,
    36,
    41,
    61,
    72,
    84,
    98
   ],
   [
    12,
    15,
    25,
    37,
    85,
    87,
    105,
    119
   ],
   [
    16,
    26,
    38,
    45,
    73,
    86,
    88,
    106
   ],
   [
    5,
    27,
    31,
    39,
    74,
    87,
    92,
    101
   ],
   [
    28,
    32,
    36,
    40,
    75,
    88,
    107,
    118
   ],
   [
    29,
    37,
    41,
    58,
    68,
    76,
    89,
    108
   ],
   [
    0,
    28,
    30,
    42,
    64,
    89,
    90,
    104
   ],
   [
    21,
    29,
    31,
    43,
    78,
    91,
    93,
    117
   ],
   [
    22,
    32,
    44,
    57,
    66,
    79,
    92,
    94
   ],
   [
    9,
    33,
    45,
    48,
    60,
    80,
    93,
    109
   ],
   [
    34,
    42,
    46,
    49,
    81,
    84,
    94,
    112
   ],
   [
    0,
    24,
    35,
    43,
    82,
    85,
    95,
    113
   ],
   [
    1,
    22,
    36,
    47,
    67,
    83,
    96,
    109
   ],
   [
    23,
    27,
    37,
    48,
    84,
    97,
    99,
    114
   ],
   [
    28,
    38,
    49,
    54,
    63,
    85,
    98,
    100
   ],
   [
    14,
    39,
    43,
    50,
    61,
    86,
    99,
    104
   ],
   [
    40,
    44,
    47,
    51,
    78,
    87,
    100,
    115
   ],
   [
    1,
    18,
    41,
    48,
    79,
    88,
    101,
    116
   ],
   [
    4,
    40,
    42,
    52,
    62,
    72,
    101,
    102
   ],
   [
    33,
    41,
    43,
    53,
    75,
    90,
    103,
    105
   ],
   [
    2,
    15,
    34,
    44,
    76,
    91,
    104,
    106
   ],
   [
    20,
    45,
    54,
    56,
    64,
    65,
    92,
    105
   ],
   [
    3,
    5,
    46,
    52,
    93,
    96,
    106,
    118
   ],
   [
    7,
    34,
    47,
    55,
    65,
    77,
    95,
    107
   ],
   [
    35,
    39,
    48,
    56,
    70,
    96,
    108,
    110
   ],
   [
    5,
    10,
    40,
    49,
    71,
    97,
    109,
    111
   ],
   [
    26,
    50,
    53,
    57,
    62,
    67,
    98,
    110
   ],
   [
    2,
    6,
    51,
    55,
    90,
    99,
    111,
    119
   ],
   [
    12,
    51,
    52,
    58,
    61,
    69,
    83,
    112
   ],
   [
    1,
    8,
    45,
    53,
    87,
    102,
    113,
    114
   ],
   [
    10,
    13,
    32,
    54,
    72,
    74,
    104,
    114
   ],
   [
    17,
    46,
    55,
    59,
    60,
    74,
    89,
    115
   ],
   [
    0,
    13,
    50,
    56,
    81,
    107,
    116,
    117
   ],
   [
    8,
    15,
    38,
    57,
    69,
    77,
    109,
    117
   ],
   [
    6,
    18,
    23,
    58,
    67,
    80,
    95,
    118
   ],
   [
    3,
    24,
    29,
    59,
    64,
    86,
    101,
    119
   ]
  ]
 },
 "distance": {
  "d": 14,
  "X": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    6,
    21,
    22,
    26,
    41,
    43,
    67,
    79,
    85,
    86,
    98,
    108,
    110,
    119
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1022
    ]
   }
  },
  "Z": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    5,
    13,
    15,
    17,
    20,
    26,
    29,
    33,
    49,
    59,
    60,
    76,
    84,
    115
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1023
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C30 x C2 = SmallGroup(60, 13) (order 60), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 120; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 8, 34, 37}, b = {0, 4, 36, 53} as element indices. Check weight 8. 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"
}
