{
 "schema_version": "0.2",
 "name": "[[180,20,11]] two-block code over C15 x S3",
 "code_type": "CSS",
 "n": 180,
 "k": 20,
 "checks": {
  "X": [
   [
    0,
    8,
    44,
    61,
    90,
    120,
    165
   ],
   [
    1,
    14,
    34,
    52,
    91,
    112,
    171
   ],
   [
    0,
    2,
    59,
    74,
    92,
    135,
    174
   ],
   [
    3,
    20,
    61,
    75,
    93,
    103,
    138
   ],
   [
    4,
    11,
    21,
    25,
    94,
    132,
    157
   ],
   [
    1,
    5,
    49,
    66,
    95,
    126,
    177
   ],
   [
    6,
    28,
    52,
    68,
    96,
    109,
    129
   ],
   [
    7,
    29,
    53,
    69,
    97,
    141,
    149
   ],
   [
    2,
    8,
    72,
    83,
    98,
    107,
    178
   ],
   [
    3,
    9,
    74,
    84,
    99,
    114,
    152
   ],
   [
    4,
    10,
    22,
    39,
    100,
    147,
    168
   ],
   [
    11,
    13,
    36,
    75,
    101,
    117,
    155
   ],
   [
    12,
    25,
    37,
    42,
    90,
    102,
    170
   ],
   [
    13,
    26,
    38,
    43,
    103,
    139,
    150
   ],
   [
    5,
    14,
    63,
    77,
    101,
    104,
    179
   ],
   [
    6,
    15,
    66,
    79,
    105,
    122,
    144
   ],
   [
    7,
    16,
    67,
    80,
    106,
    155,
    162
   ],
   [
    7,
    17,
    45,
    68,
    107,
    125,
    147
   ],
   [
    18,
    46,
    69,
    81,
    91,
    108,
    164
   ],
   [
    17,
    19,
    33,
    47,
    109,
    130,
    158
   ],
   [
    9,
    20,
    83,
    88,
    110,
    123,
    128
   ],
   [
    10,
    21,
    36,
    54,
    111,
    143,
    160
   ],
   [
    11,
    22,
    24,
    84,
    112,
    131,
    166
   ],
   [
    12,
    23,
    39,
    57,
    92,
    113,
    176
   ],
   [
    13,
    24,
    40,
    58,
    114,
    153,
    163
   ],
   [
    13,
    25,
    27,
    54,
    95,
    115,
    134
   ],
   [
    0,
    26,
    42,
    55,
    93,
    116,
    177
   ],
   [
    27,
    43,
    56,
    60,
    94,
    117,
    156
   ],
   [
    15,
    28,
    77,
    85,
    115,
    118,
    137
   ],
   [
    16,
    29,
    78,
    86,
    119,
    134,
    166
   ],
   [
    16,
    17,
    30,
    79,
    120,
    140,
    160
   ],
   [
    18,
    31,
    80,
    87,
    95,
    121,
    173
   ],
   [
    19,
    30,
    32,
    48,
    122,
    145,
    169
   ],
   [
    7,
    18,
    33,
    62,
    92,
    123,
    143
   ],
   [
    19,
    34,
    63,
    81,
    96,
    124,
    174
   ],
   [
    33,
    35,
    51,
    64,
    97,
    125,
    148
   ],
   [
    22,
    36,
    38,
    88,
    126,
    141,
    146
   ],
   [
    23,
    37,
    54,
    70,
    98,
    127,
    159
   ],
   [
    24,
    38,
    55,
    71,
    124,
    128,
    172
   ],
   [
    24,
    25,
    39,
    41,
    104,
    129,
    149
   ],
   [
    2,
    26,
    40,
    57,
    99,
    130,
    179
   ],
   [
    27,
    41,
    58,
    73,
    100,
    131,
    167
   ],
   [
    27,
    42,
    44,
    70,
    105,
    132,
    151
   ],
   [
    0,
    3,
    43,
    71,
    101,
    122,
    133
   ],
   [
    4,
    44,
    60,
    72,
    102,
    134,
    169
   ],
   [
    29,
    30,
    45,
    85,
    132,
    135,
    154
   ],
   [
    31,
    46,
    86,
    89,
    104,
    136,
    151
   ],
   [
    32,
    45,
    47,
    62,
    116,
    137,
    175
   ],
   [
    16,
    31,
    33,
    48,
    98,
    138,
    157
   ],
   [
    32,
    34,
    49,
    87,
    105,
    139,
    178
   ],
   [
    35,
    48,
    50,
    65,
    106,
    140,
    161
   ],
   [
    18,
    34,
    51,
    76,
    99,
    141,
    159
   ],
   [
    19,
    35,
    52,
    77,
    107,
    114,
    142
   ],
   [
    1,
    51,
    53,
    78,
    108,
    143,
    163
   ],
   [
    38,
    39,
    54,
    56,
    91,
    144,
    162
   ],
   [
    8,
    40,
    55,
    70,
    110,
    145,
    171
   ],
   [
    41,
    56,
    71,
    82,
    111,
    142,
    146
   ],
   [
    41,
    42,
    57,
    59,
    118,
    147,
    164
   ],
   [
    2,
    9,
    43,
    58,
    112,
    137,
    148
   ],
   [
    10,
    44,
    59,
    73,
    113,
    149,
    175
   ],
   [
    3,
    11,
    60,
    82,
    115,
    140,
    150
   ],
   [
    4,
    12,
    61,
    83,
    106,
    116,
    151
   ],
   [
    29,
    46,
    48,
    62,
    90,
    152,
    168
   ],
   [
    47,
    49,
    63,
    89,
    118,
    153,
    165
   ],
   [
    50,
    62,
    64,
    76,
    119,
    133,
    154
   ],
   [
    31,
    49,
    51,
    65,
    110,
    155,
    170
   ],
   [
    32,
    50,
    52,
    66,
    120,
    128,
    156
   ],
   [
    5,
    53,
    65,
    67,
    121,
    157,
    172
   ],
   [
    35,
    53,
    68,
    85,
    123,
    131,
    158
   ],
   [
    1,
    6,
    69,
    86,
    100,
    124,
    159
   ],
   [
    56,
    57,
    70,
    72,
    96,
    160,
    173
   ],
   [
    8,
    20,
    58,
    71,
    109,
    126,
    161
   ],
   [
    21,
    59,
    72,
    82,
    127,
    158,
    162
   ],
   [
    9,
    22,
    60,
    73,
    129,
    154,
    163
   ],
   [
    10,
    23,
    61,
    74,
    119,
    130,
    164
   ],
   [
    12,
    26,
    75,
    88,
    121,
    133,
    165
   ],
   [
    46,
    63,
    65,
    76,
    93,
    166,
    176
   ],
   [
    47,
    64,
    66,
    77,
    103,
    135,
    167
   ],
   [
    14,
    67,
    76,
    78,
    136,
    150,
    168
   ],
   [
    50,
    67,
    68,
    79,
    138,
    146,
    169
   ],
   [
    5,
    15,
    69,
    80,
    111,
    139,
    170
   ],
   [
    6,
    17,
    81,
    89,
    113,
    142,
    171
   ],
   [
    20,
    36,
    73,
    82,
    125,
    144,
    172
   ],
   [
    21,
    37,
    74,
    83,
    97,
    145,
    173
   ],
   [
    23,
    40,
    75,
    84,
    136,
    148,
    174
   ],
   [
    64,
    78,
    79,
    85,
    117,
    152,
    175
   ],
   [
    14,
    28,
    80,
    86,
    94,
    153,
    176
   ],
   [
    15,
    30,
    81,
    87,
    127,
    156,
    177
   ],
   [
    37,
    55,
    84,
    88,
    108,
    161,
    178
   ],
   [
    28,
    45,
    87,
    89,
    102,
    167,
    179
   ]
  ],
  "Z": [
   [
    0,
    12,
    62,
    90,
    92,
    116,
    133
   ],
   [
    1,
    18,
    54,
    91,
    95,
    143,
    159
   ],
   [
    2,
    23,
    33,
    92,
    98,
    130,
    148
   ],
   [
    3,
    26,
    76,
    93,
    99,
    133,
    150
   ],
   [
    4,
    27,
    86,
    94,
    100,
    134,
    151
   ],
   [
    5,
    25,
    31,
    95,
    104,
    157,
    170
   ],
   [
    6,
    34,
    70,
    96,
    105,
    159,
    171
   ],
   [
    7,
    35,
    83,
    97,
    106,
    107,
    123
   ],
   [
    8,
    37,
    48,
    90,
    98,
    145,
    161
   ],
   [
    9,
    40,
    51,
    99,
    110,
    148,
    163
   ],
   [
    10,
    41,
    69,
    100,
    111,
    149,
    164
   ],
   [
    11,
    14,
    43,
    94,
    101,
    112,
    150
   ],
   [
    12,
    44,
    89,
    102,
    113,
    151,
    165
   ],
   [
    3,
    13,
    77,
    101,
    103,
    114,
    115
   ],
   [
    14,
    39,
    46,
    91,
    104,
    168,
    176
   ],
   [
    15,
    42,
    49,
    105,
    118,
    170,
    177
   ],
   [
    16,
    50,
    61,
    106,
    119,
    120,
    138
   ],
   [
    8,
    17,
    52,
    107,
    109,
    120,
    171
   ],
   [
    18,
    53,
    88,
    108,
    121,
    123,
    141
   ],
   [
    6,
    19,
    71,
    109,
    122,
    124,
    142
   ],
   [
    20,
    55,
    65,
    93,
    110,
    161,
    172
   ],
   [
    21,
    56,
    80,
    94,
    111,
    162,
    173
   ],
   [
    1,
    22,
    58,
    100,
    112,
    126,
    163
   ],
   [
    23,
    59,
    81,
    113,
    127,
    164,
    174
   ],
   [
    9,
    24,
    52,
    112,
    114,
    128,
    129
   ],
   [
    25,
    28,
    60,
    94,
    102,
    115,
    129
   ],
   [
    26,
    47,
    61,
    103,
    116,
    130,
    165
   ],
   [
    11,
    27,
    85,
    115,
    117,
    131,
    132
   ],
   [
    28,
    57,
    63,
    96,
    118,
    176,
    179
   ],
   [
    29,
    64,
    74,
    97,
    119,
    135,
    152
   ],
   [
    0,
    30,
    66,
    120,
    122,
    135,
    177
   ],
   [
    31,
    67,
    75,
    121,
    136,
    138,
    155
   ],
   [
    15,
    32,
    43,
    122,
    137,
    139,
    156
   ],
   [
    20,
    33,
    68,
    109,
    123,
    125,
    138
   ],
   [
    34,
    38,
    69,
    91,
    124,
    139,
    141
   ],
   [
    17,
    35,
    82,
    125,
    140,
    142,
    158
   ],
   [
    5,
    36,
    71,
    101,
    111,
    126,
    172
   ],
   [
    37,
    72,
    87,
    102,
    127,
    173,
    178
   ],
   [
    20,
    38,
    66,
    103,
    126,
    128,
    144
   ],
   [
    6,
    39,
    73,
    100,
    113,
    129,
    144
   ],
   [
    19,
    40,
    74,
    114,
    130,
    145,
    174
   ],
   [
    22,
    41,
    68,
    129,
    131,
    146,
    147
   ],
   [
    4,
    42,
    45,
    102,
    116,
    132,
    147
   ],
   [
    43,
    64,
    75,
    103,
    117,
    133,
    148
   ],
   [
    25,
    29,
    44,
    90,
    132,
    134,
    149
   ],
   [
    2,
    45,
    77,
    107,
    135,
    137,
    179
   ],
   [
    46,
    78,
    84,
    108,
    136,
    152,
    166
   ],
   [
    28,
    47,
    58,
    109,
    137,
    153,
    167
   ],
   [
    3,
    48,
    79,
    122,
    138,
    140,
    152
   ],
   [
    13,
    49,
    80,
    95,
    139,
    153,
    155
   ],
   [
    30,
    50,
    60,
    140,
    154,
    156,
    169
   ],
   [
    7,
    36,
    51,
    125,
    141,
    143,
    155
   ],
   [
    52,
    56,
    81,
    91,
    96,
    142,
    156
   ],
   [
    21,
    33,
    53,
    97,
    143,
    157,
    158
   ],
   [
    15,
    54,
    82,
    111,
    115,
    127,
    144
   ],
   [
    32,
    55,
    83,
    116,
    128,
    145,
    178
   ],
   [
    36,
    56,
    79,
    117,
    144,
    146,
    160
   ],
   [
    10,
    17,
    57,
    113,
    130,
    147,
    160
   ],
   [
    35,
    58,
    84,
    114,
    131,
    148,
    161
   ],
   [
    7,
    39,
    59,
    92,
    147,
    149,
    162
   ],
   [
    13,
    60,
    78,
    117,
    134,
    150,
    163
   ],
   [
    42,
    46,
    61,
    90,
    93,
    151,
    164
   ],
   [
    9,
    62,
    85,
    123,
    137,
    152,
    154
   ],
   [
    24,
    63,
    86,
    104,
    124,
    153,
    166
   ],
   [
    45,
    64,
    73,
    125,
    154,
    167,
    175
   ],
   [
    11,
    16,
    65,
    140,
    155,
    157,
    166
   ],
   [
    27,
    66,
    87,
    95,
    105,
    156,
    167
   ],
   [
    4,
    48,
    67,
    106,
    157,
    168,
    169
   ],
   [
    19,
    68,
    72,
    96,
    107,
    158,
    169
   ],
   [
    37,
    51,
    69,
    97,
    108,
    159,
    170
   ],
   [
    21,
    30,
    70,
    127,
    132,
    145,
    160
   ],
   [
    50,
    71,
    88,
    128,
    133,
    146,
    161
   ],
   [
    16,
    54,
    72,
    98,
    134,
    160,
    162
   ],
   [
    24,
    53,
    73,
    131,
    149,
    163,
    172
   ],
   [
    18,
    57,
    74,
    92,
    99,
    164,
    173
   ],
   [
    0,
    63,
    75,
    93,
    101,
    165,
    174
   ],
   [
    22,
    29,
    76,
    141,
    154,
    166,
    168
   ],
   [
    41,
    77,
    89,
    104,
    118,
    142,
    167
   ],
   [
    10,
    62,
    78,
    119,
    143,
    168,
    175
   ],
   [
    32,
    44,
    79,
    105,
    120,
    169,
    175
   ],
   [
    12,
    65,
    80,
    106,
    121,
    170,
    176
   ],
   [
    1,
    55,
    81,
    108,
    124,
    171,
    177
   ],
   [
    38,
    67,
    82,
    146,
    150,
    162,
    172
   ],
   [
    31,
    70,
    83,
    98,
    110,
    151,
    173
   ],
   [
    2,
    34,
    84,
    99,
    112,
    174,
    178
   ],
   [
    47,
    59,
    85,
    118,
    135,
    158,
    175
   ],
   [
    23,
    76,
    86,
    119,
    136,
    159,
    176
   ],
   [
    5,
    26,
    87,
    121,
    139,
    177,
    179
   ],
   [
    8,
    49,
    88,
    110,
    126,
    165,
    178
   ],
   [
    14,
    40,
    89,
    136,
    153,
    171,
    179
   ]
  ]
 },
 "distance": {
  "d": 11,
  "X": {
   "value": 11,
   "confidence": "upper_bound",
   "witness": [
    7,
    35,
    36,
    82,
    111,
    131,
    132,
    147,
    149,
    160,
    162
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1023
    ]
   }
  },
  "Z": {
   "value": 11,
   "confidence": "upper_bound",
   "witness": [
    16,
    51,
    64,
    65,
    67,
    76,
    78,
    103,
    138,
    140,
    150
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1024
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C15 x S3 = SmallGroup(90, 6) (order 90), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 180; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 2, 26, 43}, b = {0, 12, 62} as element indices. Check weight 7. 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"
}
