{
 "schema_version": "0.2",
 "name": "[[146,18,14]] two-block code over C73",
 "code_type": "CSS",
 "n": 146,
 "k": 18,
 "checks": {
  "X": [
   [
    0,
    9,
    17,
    57,
    72,
    73,
    104,
    133
   ],
   [
    0,
    1,
    10,
    18,
    58,
    74,
    105,
    134
   ],
   [
    1,
    2,
    11,
    19,
    59,
    75,
    106,
    135
   ],
   [
    2,
    3,
    12,
    20,
    60,
    76,
    107,
    136
   ],
   [
    3,
    4,
    13,
    21,
    61,
    77,
    108,
    137
   ],
   [
    4,
    5,
    14,
    22,
    62,
    78,
    109,
    138
   ],
   [
    5,
    6,
    15,
    23,
    63,
    79,
    110,
    139
   ],
   [
    6,
    7,
    16,
    24,
    64,
    80,
    111,
    140
   ],
   [
    7,
    8,
    17,
    25,
    65,
    81,
    112,
    141
   ],
   [
    8,
    9,
    18,
    26,
    66,
    82,
    113,
    142
   ],
   [
    9,
    10,
    19,
    27,
    67,
    83,
    114,
    143
   ],
   [
    10,
    11,
    20,
    28,
    68,
    84,
    115,
    144
   ],
   [
    11,
    12,
    21,
    29,
    69,
    85,
    116,
    145
   ],
   [
    12,
    13,
    22,
    30,
    70,
    73,
    86,
    117
   ],
   [
    13,
    14,
    23,
    31,
    71,
    74,
    87,
    118
   ],
   [
    14,
    15,
    24,
    32,
    72,
    75,
    88,
    119
   ],
   [
    0,
    15,
    16,
    25,
    33,
    76,
    89,
    120
   ],
   [
    1,
    16,
    17,
    26,
    34,
    77,
    90,
    121
   ],
   [
    2,
    17,
    18,
    27,
    35,
    78,
    91,
    122
   ],
   [
    3,
    18,
    19,
    28,
    36,
    79,
    92,
    123
   ],
   [
    4,
    19,
    20,
    29,
    37,
    80,
    93,
    124
   ],
   [
    5,
    20,
    21,
    30,
    38,
    81,
    94,
    125
   ],
   [
    6,
    21,
    22,
    31,
    39,
    82,
    95,
    126
   ],
   [
    7,
    22,
    23,
    32,
    40,
    83,
    96,
    127
   ],
   [
    8,
    23,
    24,
    33,
    41,
    84,
    97,
    128
   ],
   [
    9,
    24,
    25,
    34,
    42,
    85,
    98,
    129
   ],
   [
    10,
    25,
    26,
    35,
    43,
    86,
    99,
    130
   ],
   [
    11,
    26,
    27,
    36,
    44,
    87,
    100,
    131
   ],
   [
    12,
    27,
    28,
    37,
    45,
    88,
    101,
    132
   ],
   [
    13,
    28,
    29,
    38,
    46,
    89,
    102,
    133
   ],
   [
    14,
    29,
    30,
    39,
    47,
    90,
    103,
    134
   ],
   [
    15,
    30,
    31,
    40,
    48,
    91,
    104,
    135
   ],
   [
    16,
    31,
    32,
    41,
    49,
    92,
    105,
    136
   ],
   [
    17,
    32,
    33,
    42,
    50,
    93,
    106,
    137
   ],
   [
    18,
    33,
    34,
    43,
    51,
    94,
    107,
    138
   ],
   [
    19,
    34,
    35,
    44,
    52,
    95,
    108,
    139
   ],
   [
    20,
    35,
    36,
    45,
    53,
    96,
    109,
    140
   ],
   [
    21,
    36,
    37,
    46,
    54,
    97,
    110,
    141
   ],
   [
    22,
    37,
    38,
    47,
    55,
    98,
    111,
    142
   ],
   [
    23,
    38,
    39,
    48,
    56,
    99,
    112,
    143
   ],
   [
    24,
    39,
    40,
    49,
    57,
    100,
    113,
    144
   ],
   [
    25,
    40,
    41,
    50,
    58,
    101,
    114,
    145
   ],
   [
    26,
    41,
    42,
    51,
    59,
    73,
    102,
    115
   ],
   [
    27,
    42,
    43,
    52,
    60,
    74,
    103,
    116
   ],
   [
    28,
    43,
    44,
    53,
    61,
    75,
    104,
    117
   ],
   [
    29,
    44,
    45,
    54,
    62,
    76,
    105,
    118
   ],
   [
    30,
    45,
    46,
    55,
    63,
    77,
    106,
    119
   ],
   [
    31,
    46,
    47,
    56,
    64,
    78,
    107,
    120
   ],
   [
    32,
    47,
    48,
    57,
    65,
    79,
    108,
    121
   ],
   [
    33,
    48,
    49,
    58,
    66,
    80,
    109,
    122
   ],
   [
    34,
    49,
    50,
    59,
    67,
    81,
    110,
    123
   ],
   [
    35,
    50,
    51,
    60,
    68,
    82,
    111,
    124
   ],
   [
    36,
    51,
    52,
    61,
    69,
    83,
    112,
    125
   ],
   [
    37,
    52,
    53,
    62,
    70,
    84,
    113,
    126
   ],
   [
    38,
    53,
    54,
    63,
    71,
    85,
    114,
    127
   ],
   [
    39,
    54,
    55,
    64,
    72,
    86,
    115,
    128
   ],
   [
    0,
    40,
    55,
    56,
    65,
    87,
    116,
    129
   ],
   [
    1,
    41,
    56,
    57,
    66,
    88,
    117,
    130
   ],
   [
    2,
    42,
    57,
    58,
    67,
    89,
    118,
    131
   ],
   [
    3,
    43,
    58,
    59,
    68,
    90,
    119,
    132
   ],
   [
    4,
    44,
    59,
    60,
    69,
    91,
    120,
    133
   ],
   [
    5,
    45,
    60,
    61,
    70,
    92,
    121,
    134
   ],
   [
    6,
    46,
    61,
    62,
    71,
    93,
    122,
    135
   ],
   [
    7,
    47,
    62,
    63,
    72,
    94,
    123,
    136
   ],
   [
    0,
    8,
    48,
    63,
    64,
    95,
    124,
    137
   ],
   [
    1,
    9,
    49,
    64,
    65,
    96,
    125,
    138
   ],
   [
    2,
    10,
    50,
    65,
    66,
    97,
    126,
    139
   ],
   [
    3,
    11,
    51,
    66,
    67,
    98,
    127,
    140
   ],
   [
    4,
    12,
    52,
    67,
    68,
    99,
    128,
    141
   ],
   [
    5,
    13,
    53,
    68,
    69,
    100,
    129,
    142
   ],
   [
    6,
    14,
    54,
    69,
    70,
    101,
    130,
    143
   ],
   [
    7,
    15,
    55,
    70,
    71,
    102,
    131,
    144
   ],
   [
    8,
    16,
    56,
    71,
    72,
    103,
    132,
    145
   ]
  ],
  "Z": [
   [
    0,
    13,
    42,
    73,
    74,
    89,
    129,
    137
   ],
   [
    1,
    14,
    43,
    74,
    75,
    90,
    130,
    138
   ],
   [
    2,
    15,
    44,
    75,
    76,
    91,
    131,
    139
   ],
   [
    3,
    16,
    45,
    76,
    77,
    92,
    132,
    140
   ],
   [
    4,
    17,
    46,
    77,
    78,
    93,
    133,
    141
   ],
   [
    5,
    18,
    47,
    78,
    79,
    94,
    134,
    142
   ],
   [
    6,
    19,
    48,
    79,
    80,
    95,
    135,
    143
   ],
   [
    7,
    20,
    49,
    80,
    81,
    96,
    136,
    144
   ],
   [
    8,
    21,
    50,
    81,
    82,
    97,
    137,
    145
   ],
   [
    9,
    22,
    51,
    73,
    82,
    83,
    98,
    138
   ],
   [
    10,
    23,
    52,
    74,
    83,
    84,
    99,
    139
   ],
   [
    11,
    24,
    53,
    75,
    84,
    85,
    100,
    140
   ],
   [
    12,
    25,
    54,
    76,
    85,
    86,
    101,
    141
   ],
   [
    13,
    26,
    55,
    77,
    86,
    87,
    102,
    142
   ],
   [
    14,
    27,
    56,
    78,
    87,
    88,
    103,
    143
   ],
   [
    15,
    28,
    57,
    79,
    88,
    89,
    104,
    144
   ],
   [
    16,
    29,
    58,
    80,
    89,
    90,
    105,
    145
   ],
   [
    17,
    30,
    59,
    73,
    81,
    90,
    91,
    106
   ],
   [
    18,
    31,
    60,
    74,
    82,
    91,
    92,
    107
   ],
   [
    19,
    32,
    61,
    75,
    83,
    92,
    93,
    108
   ],
   [
    20,
    33,
    62,
    76,
    84,
    93,
    94,
    109
   ],
   [
    21,
    34,
    63,
    77,
    85,
    94,
    95,
    110
   ],
   [
    22,
    35,
    64,
    78,
    86,
    95,
    96,
    111
   ],
   [
    23,
    36,
    65,
    79,
    87,
    96,
    97,
    112
   ],
   [
    24,
    37,
    66,
    80,
    88,
    97,
    98,
    113
   ],
   [
    25,
    38,
    67,
    81,
    89,
    98,
    99,
    114
   ],
   [
    26,
    39,
    68,
    82,
    90,
    99,
    100,
    115
   ],
   [
    27,
    40,
    69,
    83,
    91,
    100,
    101,
    116
   ],
   [
    28,
    41,
    70,
    84,
    92,
    101,
    102,
    117
   ],
   [
    29,
    42,
    71,
    85,
    93,
    102,
    103,
    118
   ],
   [
    30,
    43,
    72,
    86,
    94,
    103,
    104,
    119
   ],
   [
    0,
    31,
    44,
    87,
    95,
    104,
    105,
    120
   ],
   [
    1,
    32,
    45,
    88,
    96,
    105,
    106,
    121
   ],
   [
    2,
    33,
    46,
    89,
    97,
    106,
    107,
    122
   ],
   [
    3,
    34,
    47,
    90,
    98,
    107,
    108,
    123
   ],
   [
    4,
    35,
    48,
    91,
    99,
    108,
    109,
    124
   ],
   [
    5,
    36,
    49,
    92,
    100,
    109,
    110,
    125
   ],
   [
    6,
    37,
    50,
    93,
    101,
    110,
    111,
    126
   ],
   [
    7,
    38,
    51,
    94,
    102,
    111,
    112,
    127
   ],
   [
    8,
    39,
    52,
    95,
    103,
    112,
    113,
    128
   ],
   [
    9,
    40,
    53,
    96,
    104,
    113,
    114,
    129
   ],
   [
    10,
    41,
    54,
    97,
    105,
    114,
    115,
    130
   ],
   [
    11,
    42,
    55,
    98,
    106,
    115,
    116,
    131
   ],
   [
    12,
    43,
    56,
    99,
    107,
    116,
    117,
    132
   ],
   [
    13,
    44,
    57,
    100,
    108,
    117,
    118,
    133
   ],
   [
    14,
    45,
    58,
    101,
    109,
    118,
    119,
    134
   ],
   [
    15,
    46,
    59,
    102,
    110,
    119,
    120,
    135
   ],
   [
    16,
    47,
    60,
    103,
    111,
    120,
    121,
    136
   ],
   [
    17,
    48,
    61,
    104,
    112,
    121,
    122,
    137
   ],
   [
    18,
    49,
    62,
    105,
    113,
    122,
    123,
    138
   ],
   [
    19,
    50,
    63,
    106,
    114,
    123,
    124,
    139
   ],
   [
    20,
    51,
    64,
    107,
    115,
    124,
    125,
    140
   ],
   [
    21,
    52,
    65,
    108,
    116,
    125,
    126,
    141
   ],
   [
    22,
    53,
    66,
    109,
    117,
    126,
    127,
    142
   ],
   [
    23,
    54,
    67,
    110,
    118,
    127,
    128,
    143
   ],
   [
    24,
    55,
    68,
    111,
    119,
    128,
    129,
    144
   ],
   [
    25,
    56,
    69,
    112,
    120,
    129,
    130,
    145
   ],
   [
    26,
    57,
    70,
    73,
    113,
    121,
    130,
    131
   ],
   [
    27,
    58,
    71,
    74,
    114,
    122,
    131,
    132
   ],
   [
    28,
    59,
    72,
    75,
    115,
    123,
    132,
    133
   ],
   [
    0,
    29,
    60,
    76,
    116,
    124,
    133,
    134
   ],
   [
    1,
    30,
    61,
    77,
    117,
    125,
    134,
    135
   ],
   [
    2,
    31,
    62,
    78,
    118,
    126,
    135,
    136
   ],
   [
    3,
    32,
    63,
    79,
    119,
    127,
    136,
    137
   ],
   [
    4,
    33,
    64,
    80,
    120,
    128,
    137,
    138
   ],
   [
    5,
    34,
    65,
    81,
    121,
    129,
    138,
    139
   ],
   [
    6,
    35,
    66,
    82,
    122,
    130,
    139,
    140
   ],
   [
    7,
    36,
    67,
    83,
    123,
    131,
    140,
    141
   ],
   [
    8,
    37,
    68,
    84,
    124,
    132,
    141,
    142
   ],
   [
    9,
    38,
    69,
    85,
    125,
    133,
    142,
    143
   ],
   [
    10,
    39,
    70,
    86,
    126,
    134,
    143,
    144
   ],
   [
    11,
    40,
    71,
    87,
    127,
    135,
    144,
    145
   ],
   [
    12,
    41,
    72,
    73,
    88,
    128,
    136,
    145
   ]
  ]
 },
 "distance": {
  "d": 14,
  "X": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    0,
    1,
    14,
    21,
    29,
    65,
    95,
    96,
    103,
    119,
    129,
    135,
    136,
    145
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1012
    ]
   }
  },
  "Z": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    4,
    27,
    29,
    38,
    43,
    44,
    47,
    78,
    94,
    99,
    108,
    114,
    132,
    145
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1013
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C73 = SmallGroup(73, 1) (order 73), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 146; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 1, 16, 56, 64}, b = {0, 13, 42} 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"
}