{
 "schema_version": "0.2",
 "name": "[[240,10,7]] two-block code over C3 x (C5 : C8)",
 "code_type": "CSS",
 "n": 240,
 "k": 10,
 "checks": {
  "X": [
   [
    0,
    60,
    79,
    120,
    128
   ],
   [
    1,
    10,
    67,
    121,
    134
   ],
   [
    2,
    22,
    97,
    122,
    140
   ],
   [
    3,
    18,
    30,
    123,
    142
   ],
   [
    4,
    37,
    100,
    121,
    124
   ],
   [
    2,
    5,
    83,
    125,
    166
   ],
   [
    0,
    6,
    86,
    126,
    149
   ],
   [
    7,
    26,
    65,
    120,
    127
   ],
   [
    8,
    27,
    89,
    123,
    128
   ],
   [
    9,
    28,
    90,
    129,
    176
   ],
   [
    10,
    40,
    59,
    130,
    158
   ],
   [
    1,
    11,
    49,
    131,
    160
   ],
   [
    7,
    12,
    112,
    126,
    132
   ],
   [
    10,
    13,
    44,
    133,
    186
   ],
   [
    14,
    38,
    52,
    127,
    134
   ],
   [
    15,
    39,
    53,
    135,
    188
   ],
   [
    12,
    16,
    61,
    136,
    145
   ],
   [
    13,
    17,
    102,
    137,
    213
   ],
   [
    2,
    18,
    47,
    138,
    168
   ],
   [
    3,
    19,
    84,
    122,
    139
   ],
   [
    4,
    20,
    104,
    131,
    140
   ],
   [
    5,
    21,
    105,
    141,
    196
   ],
   [
    22,
    48,
    87,
    124,
    142
   ],
   [
    23,
    49,
    88,
    137,
    143
   ],
   [
    24,
    50,
    108,
    144,
    154
   ],
   [
    6,
    25,
    51,
    145,
    221
   ],
   [
    6,
    15,
    26,
    146,
    180
   ],
   [
    19,
    27,
    82,
    138,
    147
   ],
   [
    0,
    28,
    64,
    148,
    205
   ],
   [
    8,
    29,
    72,
    139,
    149
   ],
   [
    9,
    30,
    73,
    150,
    207
   ],
   [
    23,
    27,
    31,
    151,
    163
   ],
   [
    28,
    32,
    68,
    152,
    228
   ],
   [
    33,
    62,
    76,
    153,
    165
   ],
   [
    34,
    63,
    77,
    154,
    229
   ],
   [
    31,
    35,
    84,
    155,
    191
   ],
   [
    32,
    36,
    114,
    144,
    156
   ],
   [
    11,
    37,
    45,
    130,
    157
   ],
   [
    12,
    38,
    70,
    146,
    158
   ],
   [
    13,
    39,
    71,
    159,
    214
   ],
   [
    14,
    40,
    102,
    132,
    160
   ],
   [
    15,
    41,
    103,
    152,
    161
   ],
   [
    16,
    42,
    116,
    162,
    173
   ],
   [
    17,
    18,
    43,
    163,
    233
   ],
   [
    44,
    72,
    106,
    155,
    164
   ],
   [
    45,
    73,
    107,
    165,
    179
   ],
   [
    20,
    46,
    74,
    166,
    201
   ],
   [
    21,
    47,
    75,
    153,
    167
   ],
   [
    20,
    33,
    48,
    157,
    168
   ],
   [
    21,
    34,
    49,
    169,
    222
   ],
   [
    4,
    41,
    50,
    170,
    183
   ],
   [
    5,
    51,
    87,
    171,
    236
   ],
   [
    24,
    52,
    94,
    172,
    185
   ],
   [
    25,
    53,
    95,
    173,
    237
   ],
   [
    45,
    50,
    54,
    174,
    210
   ],
   [
    51,
    55,
    91,
    162,
    175
   ],
   [
    56,
    85,
    98,
    176,
    212
   ],
   [
    57,
    86,
    99,
    164,
    177
   ],
   [
    54,
    58,
    103,
    129,
    178
   ],
   [
    55,
    59,
    119,
    179,
    190
   ],
   [
    29,
    60,
    68,
    147,
    180
   ],
   [
    30,
    61,
    69,
    171,
    181
   ],
   [
    31,
    62,
    93,
    182,
    193
   ],
   [
    1,
    32,
    63,
    183,
    238
   ],
   [
    33,
    64,
    114,
    174,
    184
   ],
   [
    34,
    65,
    115,
    185,
    199
   ],
   [
    35,
    38,
    66,
    186,
    219
   ],
   [
    36,
    39,
    67,
    172,
    187
   ],
   [
    68,
    94,
    117,
    188,
    202
   ],
   [
    19,
    69,
    95,
    125,
    189
   ],
   [
    42,
    70,
    96,
    135,
    190
   ],
   [
    43,
    71,
    97,
    191,
    200
   ],
   [
    42,
    56,
    72,
    192,
    204
   ],
   [
    43,
    57,
    73,
    193,
    239
   ],
   [
    16,
    65,
    74,
    194,
    225
   ],
   [
    17,
    75,
    106,
    182,
    195
   ],
   [
    46,
    76,
    110,
    196,
    227
   ],
   [
    47,
    77,
    111,
    184,
    197
   ],
   [
    69,
    74,
    78,
    141,
    198
   ],
   [
    75,
    79,
    109,
    199,
    209
   ],
   [
    80,
    104,
    113,
    143,
    200
   ],
   [
    11,
    81,
    105,
    201,
    211
   ],
   [
    78,
    82,
    115,
    167,
    202
   ],
   [
    52,
    83,
    91,
    194,
    203
   ],
   [
    53,
    84,
    92,
    204,
    217
   ],
   [
    8,
    54,
    85,
    205,
    231
   ],
   [
    9,
    55,
    86,
    192,
    206
   ],
   [
    56,
    87,
    119,
    207,
    220
   ],
   [
    37,
    57,
    88,
    133,
    208
   ],
   [
    58,
    62,
    89,
    150,
    209
   ],
   [
    59,
    63,
    90,
    210,
    218
   ],
   [
    40,
    91,
    110,
    136,
    211
   ],
   [
    41,
    92,
    111,
    156,
    212
   ],
   [
    66,
    93,
    112,
    177,
    213
   ],
   [
    66,
    80,
    94,
    214,
    235
   ],
   [
    67,
    81,
    95,
    203,
    215
   ],
   [
    35,
    88,
    96,
    159,
    216
   ],
   [
    36,
    97,
    117,
    217,
    224
   ],
   [
    70,
    98,
    118,
    161,
    218
   ],
   [
    26,
    71,
    99,
    219,
    226
   ],
   [
    92,
    96,
    100,
    187,
    220
   ],
   [
    29,
    101,
    116,
    189,
    221
   ],
   [
    76,
    102,
    109,
    222,
    232
   ],
   [
    7,
    77,
    103,
    148,
    223
   ],
   [
    24,
    78,
    104,
    169,
    224
   ],
   [
    25,
    79,
    105,
    225,
    230
   ],
   [
    60,
    80,
    106,
    151,
    226
   ],
   [
    61,
    81,
    107,
    175,
    227
   ],
   [
    82,
    85,
    108,
    197,
    228
   ],
   [
    64,
    109,
    118,
    178,
    229
   ],
   [
    89,
    101,
    110,
    181,
    230
   ],
   [
    3,
    90,
    111,
    231,
    234
   ],
   [
    58,
    107,
    112,
    206,
    232
   ],
   [
    48,
    93,
    113,
    208,
    233
   ],
   [
    22,
    98,
    114,
    170,
    234
   ],
   [
    23,
    99,
    115,
    195,
    235
   ],
   [
    46,
    100,
    116,
    215,
    236
   ],
   [
    83,
    101,
    117,
    198,
    237
   ],
   [
    14,
    108,
    118,
    223,
    238
   ],
   [
    44,
    113,
    119,
    216,
    239
   ]
  ],
  "Z": [
   [
    0,
    7,
    120,
    126,
    148
   ],
   [
    1,
    4,
    121,
    131,
    183
   ],
   [
    2,
    19,
    122,
    125,
    138
   ],
   [
    3,
    8,
    123,
    139,
    231
   ],
   [
    4,
    22,
    124,
    140,
    170
   ],
   [
    5,
    69,
    125,
    141,
    171
   ],
   [
    6,
    12,
    126,
    145,
    146
   ],
   [
    7,
    14,
    127,
    132,
    223
   ],
   [
    0,
    8,
    128,
    149,
    205
   ],
   [
    9,
    58,
    129,
    150,
    206
   ],
   [
    10,
    37,
    121,
    130,
    133
   ],
   [
    11,
    20,
    131,
    157,
    201
   ],
   [
    12,
    40,
    132,
    136,
    158
   ],
   [
    13,
    88,
    133,
    137,
    159
   ],
   [
    1,
    14,
    134,
    160,
    238
   ],
   [
    15,
    70,
    135,
    146,
    161
   ],
   [
    16,
    91,
    136,
    162,
    194
   ],
   [
    17,
    23,
    137,
    163,
    195
   ],
   [
    18,
    27,
    123,
    138,
    163
   ],
   [
    19,
    29,
    139,
    147,
    189
   ],
   [
    2,
    20,
    140,
    166,
    168
   ],
   [
    21,
    78,
    141,
    167,
    169
   ],
   [
    3,
    22,
    122,
    142,
    234
   ],
   [
    23,
    80,
    143,
    151,
    235
   ],
   [
    24,
    36,
    144,
    172,
    224
   ],
   [
    16,
    25,
    145,
    173,
    225
   ],
   [
    26,
    38,
    127,
    146,
    219
   ],
   [
    27,
    60,
    128,
    147,
    151
   ],
   [
    28,
    103,
    129,
    148,
    152
   ],
   [
    6,
    29,
    149,
    180,
    221
   ],
   [
    30,
    89,
    123,
    150,
    181
   ],
   [
    31,
    106,
    151,
    155,
    182
   ],
   [
    32,
    41,
    152,
    156,
    183
   ],
   [
    33,
    47,
    153,
    168,
    184
   ],
   [
    24,
    34,
    154,
    169,
    185
   ],
   [
    35,
    44,
    155,
    186,
    216
   ],
   [
    36,
    92,
    156,
    187,
    217
   ],
   [
    37,
    48,
    124,
    157,
    208
   ],
   [
    10,
    38,
    134,
    158,
    186
   ],
   [
    39,
    96,
    135,
    159,
    187
   ],
   [
    11,
    40,
    130,
    160,
    211
   ],
   [
    41,
    98,
    161,
    170,
    212
   ],
   [
    42,
    55,
    162,
    190,
    192
   ],
   [
    31,
    43,
    163,
    191,
    193
   ],
   [
    44,
    57,
    133,
    164,
    239
   ],
   [
    33,
    45,
    157,
    165,
    174
   ],
   [
    5,
    46,
    166,
    196,
    236
   ],
   [
    47,
    82,
    138,
    167,
    197
   ],
   [
    18,
    48,
    142,
    168,
    233
   ],
   [
    49,
    104,
    131,
    143,
    169
   ],
   [
    50,
    114,
    144,
    170,
    174
   ],
   [
    51,
    61,
    145,
    171,
    175
   ],
   [
    52,
    67,
    134,
    172,
    203
   ],
   [
    42,
    53,
    135,
    173,
    204
   ],
   [
    54,
    64,
    174,
    178,
    205
   ],
   [
    55,
    107,
    175,
    179,
    206
   ],
   [
    9,
    56,
    176,
    192,
    207
   ],
   [
    57,
    93,
    177,
    193,
    208
   ],
   [
    58,
    109,
    178,
    209,
    232
   ],
   [
    45,
    59,
    130,
    179,
    210
   ],
   [
    26,
    60,
    120,
    180,
    226
   ],
   [
    61,
    110,
    136,
    181,
    227
   ],
   [
    62,
    75,
    153,
    182,
    209
   ],
   [
    50,
    63,
    154,
    183,
    210
   ],
   [
    64,
    77,
    148,
    184,
    229
   ],
   [
    52,
    65,
    127,
    185,
    194
   ],
   [
    13,
    66,
    186,
    213,
    214
   ],
   [
    67,
    100,
    121,
    187,
    215
   ],
   [
    15,
    68,
    152,
    180,
    188
   ],
   [
    69,
    101,
    181,
    189,
    198
   ],
   [
    59,
    70,
    158,
    190,
    218
   ],
   [
    35,
    71,
    159,
    191,
    219
   ],
   [
    72,
    86,
    149,
    164,
    192
   ],
   [
    62,
    73,
    150,
    165,
    193
   ],
   [
    74,
    83,
    166,
    194,
    198
   ],
   [
    75,
    115,
    167,
    195,
    199
   ],
   [
    21,
    76,
    153,
    196,
    222
   ],
   [
    77,
    108,
    154,
    197,
    223
   ],
   [
    78,
    117,
    198,
    202,
    224
   ],
   [
    65,
    79,
    120,
    199,
    225
   ],
   [
    71,
    80,
    200,
    214,
    226
   ],
   [
    46,
    81,
    201,
    215,
    227
   ],
   [
    68,
    82,
    147,
    202,
    228
   ],
   [
    83,
    95,
    125,
    203,
    237
   ],
   [
    72,
    84,
    139,
    155,
    204
   ],
   [
    28,
    85,
    176,
    205,
    228
   ],
   [
    86,
    112,
    126,
    177,
    206
   ],
   [
    30,
    87,
    142,
    171,
    207
   ],
   [
    88,
    113,
    143,
    208,
    216
   ],
   [
    79,
    89,
    128,
    209,
    230
   ],
   [
    54,
    90,
    129,
    210,
    231
   ],
   [
    81,
    91,
    175,
    203,
    211
   ],
   [
    56,
    92,
    204,
    212,
    220
   ],
   [
    17,
    93,
    182,
    213,
    233
   ],
   [
    39,
    94,
    172,
    188,
    214
   ],
   [
    95,
    116,
    173,
    189,
    215
   ],
   [
    96,
    119,
    190,
    216,
    220
   ],
   [
    84,
    97,
    122,
    191,
    217
   ],
   [
    90,
    98,
    176,
    218,
    234
   ],
   [
    66,
    99,
    177,
    219,
    235
   ],
   [
    87,
    100,
    124,
    220,
    236
   ],
   [
    25,
    101,
    221,
    230,
    237
   ],
   [
    49,
    102,
    137,
    160,
    222
   ],
   [
    103,
    118,
    161,
    178,
    223
   ],
   [
    97,
    104,
    140,
    200,
    224
   ],
   [
    74,
    105,
    141,
    201,
    225
   ],
   [
    99,
    106,
    164,
    195,
    226
   ],
   [
    76,
    107,
    165,
    227,
    232
   ],
   [
    32,
    108,
    144,
    228,
    238
   ],
   [
    34,
    109,
    199,
    222,
    229
   ],
   [
    105,
    110,
    196,
    211,
    230
   ],
   [
    85,
    111,
    197,
    212,
    231
   ],
   [
    102,
    112,
    132,
    213,
    232
   ],
   [
    43,
    113,
    200,
    233,
    239
   ],
   [
    111,
    114,
    156,
    184,
    234
   ],
   [
    94,
    115,
    185,
    202,
    235
   ],
   [
    51,
    116,
    162,
    221,
    236
   ],
   [
    53,
    117,
    188,
    217,
    237
   ],
   [
    63,
    118,
    218,
    229,
    238
   ],
   [
    73,
    119,
    179,
    207,
    239
   ]
  ]
 },
 "distance": {
  "d": 7,
  "X": {
   "value": 8,
   "confidence": "upper_bound",
   "witness": [
    39,
    62,
    73,
    75,
    94,
    96,
    115,
    119
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1053
    ]
   }
  },
  "Z": {
   "value": 7,
   "confidence": "upper_bound",
   "witness": [
    71,
    99,
    155,
    164,
    191,
    214,
    235
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1054
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C3 x (C5 : C8) = SmallGroup(120, 6) (order 120), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 240; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 6, 28}, b = {0, 7} as element indices. Check weight 5. 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"
}