{
 "schema_version": "0.2",
 "name": "[[240,16,18]] two-block code over C3 x ((C10 x C2) : C2)",
 "code_type": "CSS",
 "n": 240,
 "k": 16,
 "checks": {
  "X": [
   [
    0,
    13,
    77,
    80,
    120,
    141,
    196
   ],
   [
    1,
    21,
    40,
    68,
    121,
    133,
    207
   ],
   [
    2,
    26,
    59,
    96,
    122,
    178,
    180
   ],
   [
    0,
    3,
    97,
    99,
    121,
    123,
    216
   ],
   [
    4,
    31,
    57,
    98,
    124,
    162,
    173
   ],
   [
    2,
    5,
    32,
    101,
    125,
    218,
    228
   ],
   [
    6,
    24,
    37,
    85,
    126,
    168,
    190
   ],
   [
    1,
    7,
    62,
    89,
    120,
    127,
    224
   ],
   [
    8,
    20,
    42,
    45,
    128,
    151,
    185
   ],
   [
    9,
    43,
    64,
    91,
    129,
    220,
    226
   ],
   [
    2,
    10,
    81,
    110,
    130,
    139,
    200
   ],
   [
    11,
    48,
    75,
    82,
    131,
    156,
    157
   ],
   [
    0,
    12,
    49,
    112,
    132,
    202,
    239
   ],
   [
    3,
    13,
    58,
    111,
    127,
    133,
    230
   ],
   [
    4,
    14,
    79,
    112,
    128,
    134,
    195
   ],
   [
    5,
    10,
    15,
    113,
    135,
    191,
    232
   ],
   [
    11,
    16,
    54,
    81,
    136,
    197,
    237
   ],
   [
    12,
    14,
    17,
    55,
    131,
    137,
    210
   ],
   [
    6,
    18,
    44,
    102,
    131,
    138,
    211
   ],
   [
    9,
    19,
    60,
    63,
    139,
    146,
    167
   ],
   [
    20,
    46,
    61,
    104,
    140,
    213,
    238
   ],
   [
    7,
    21,
    46,
    83,
    123,
    141,
    234
   ],
   [
    8,
    22,
    39,
    67,
    124,
    142,
    206
   ],
   [
    9,
    23,
    85,
    107,
    143,
    179,
    236
   ],
   [
    24,
    41,
    66,
    69,
    144,
    208,
    233
   ],
   [
    25,
    67,
    87,
    109,
    139,
    145,
    199
   ],
   [
    10,
    26,
    76,
    100,
    146,
    158,
    219
   ],
   [
    11,
    27,
    95,
    101,
    126,
    147,
    177
   ],
   [
    3,
    12,
    28,
    118,
    148,
    221,
    226
   ],
   [
    4,
    29,
    72,
    97,
    149,
    179,
    235
   ],
   [
    5,
    27,
    30,
    73,
    124,
    150,
    234
   ],
   [
    14,
    31,
    36,
    118,
    142,
    151,
    215
   ],
   [
    15,
    26,
    32,
    82,
    152,
    212,
    238
   ],
   [
    16,
    27,
    33,
    100,
    153,
    213,
    217
   ],
   [
    17,
    28,
    31,
    34,
    147,
    154,
    167
   ],
   [
    3,
    29,
    35,
    78,
    122,
    155,
    227
   ],
   [
    30,
    33,
    36,
    79,
    149,
    156,
    187
   ],
   [
    18,
    37,
    64,
    66,
    147,
    157,
    227
   ],
   [
    19,
    23,
    38,
    84,
    122,
    158,
    189
   ],
   [
    20,
    39,
    68,
    114,
    159,
    218,
    229
   ],
   [
    25,
    40,
    83,
    86,
    160,
    191,
    231
   ],
   [
    41,
    70,
    84,
    116,
    128,
    161,
    230
   ],
   [
    22,
    25,
    42,
    61,
    134,
    162,
    223
   ],
   [
    23,
    43,
    70,
    102,
    163,
    201,
    239
   ],
   [
    24,
    44,
    63,
    90,
    164,
    202,
    225
   ],
   [
    25,
    45,
    104,
    117,
    156,
    158,
    165
   ],
   [
    46,
    65,
    89,
    92,
    126,
    166,
    219
   ],
   [
    22,
    47,
    90,
    106,
    160,
    167,
    175
   ],
   [
    27,
    48,
    53,
    113,
    138,
    168,
    199
   ],
   [
    13,
    28,
    49,
    98,
    169,
    233,
    236
   ],
   [
    14,
    29,
    50,
    111,
    170,
    201,
    208
   ],
   [
    15,
    30,
    48,
    51,
    134,
    171,
    207
   ],
   [
    10,
    16,
    52,
    94,
    120,
    172,
    223
   ],
   [
    17,
    50,
    53,
    95,
    136,
    173,
    222
   ],
   [
    33,
    48,
    54,
    59,
    174,
    229,
    231
   ],
   [
    4,
    34,
    49,
    55,
    168,
    175,
    189
   ],
   [
    13,
    35,
    50,
    56,
    130,
    176,
    190
   ],
   [
    36,
    51,
    54,
    57,
    145,
    170,
    177
   ],
   [
    15,
    52,
    58,
    99,
    132,
    178,
    209
   ],
   [
    53,
    56,
    59,
    100,
    163,
    172,
    179
   ],
   [
    38,
    41,
    43,
    60,
    130,
    180,
    210
   ],
   [
    39,
    61,
    87,
    89,
    181,
    232,
    237
   ],
   [
    40,
    45,
    62,
    103,
    182,
    197,
    212
   ],
   [
    41,
    63,
    91,
    119,
    142,
    183,
    196
   ],
   [
    47,
    64,
    102,
    105,
    121,
    184,
    215
   ],
   [
    38,
    65,
    93,
    103,
    144,
    185,
    214
   ],
   [
    44,
    47,
    66,
    84,
    186,
    221,
    235
   ],
   [
    45,
    67,
    93,
    114,
    177,
    180,
    187
   ],
   [
    46,
    68,
    86,
    108,
    138,
    178,
    188
   ],
   [
    42,
    47,
    69,
    116,
    137,
    182,
    189
   ],
   [
    7,
    70,
    88,
    107,
    140,
    190,
    198
   ],
   [
    19,
    44,
    71,
    108,
    152,
    184,
    191
   ],
   [
    31,
    50,
    72,
    77,
    192,
    220,
    225
   ],
   [
    11,
    32,
    51,
    73,
    151,
    193,
    224
   ],
   [
    26,
    33,
    52,
    74,
    123,
    185,
    194
   ],
   [
    34,
    53,
    72,
    75,
    153,
    184,
    195
   ],
   [
    28,
    35,
    76,
    110,
    125,
    196,
    204
   ],
   [
    36,
    74,
    77,
    111,
    155,
    197,
    203
   ],
   [
    0,
    56,
    72,
    78,
    146,
    198,
    211
   ],
   [
    16,
    57,
    73,
    79,
    165,
    192,
    199
   ],
   [
    32,
    58,
    74,
    80,
    148,
    166,
    200
   ],
   [
    59,
    75,
    78,
    81,
    129,
    194,
    201
   ],
   [
    34,
    76,
    82,
    113,
    150,
    186,
    202
   ],
   [
    62,
    65,
    67,
    83,
    203,
    217,
    228
   ],
   [
    63,
    84,
    106,
    107,
    162,
    204,
    216
   ],
   [
    64,
    69,
    85,
    115,
    127,
    173,
    205
   ],
   [
    60,
    65,
    86,
    109,
    164,
    172,
    206
   ],
   [
    18,
    71,
    87,
    114,
    129,
    193,
    207
   ],
   [
    8,
    62,
    88,
    115,
    166,
    192,
    208
   ],
   [
    68,
    71,
    89,
    103,
    157,
    200,
    209
   ],
   [
    8,
    69,
    90,
    119,
    154,
    203,
    210
   ],
   [
    21,
    70,
    91,
    105,
    155,
    159,
    211
   ],
   [
    38,
    66,
    71,
    92,
    125,
    205,
    212
   ],
   [
    6,
    23,
    93,
    117,
    161,
    174,
    213
   ],
   [
    2,
    54,
    74,
    94,
    133,
    206,
    214
   ],
   [
    29,
    55,
    75,
    95,
    174,
    205,
    215
   ],
   [
    49,
    56,
    76,
    96,
    135,
    161,
    216
   ],
   [
    57,
    77,
    94,
    97,
    160,
    176,
    217
   ],
   [
    51,
    58,
    98,
    118,
    137,
    181,
    218
   ],
   [
    5,
    80,
    94,
    99,
    169,
    188,
    219
   ],
   [
    35,
    81,
    95,
    100,
    143,
    214,
    220
   ],
   [
    55,
    82,
    96,
    101,
    144,
    171,
    221
   ],
   [
    85,
    88,
    90,
    102,
    141,
    195,
    222
   ],
   [
    19,
    86,
    103,
    117,
    186,
    194,
    223
   ],
   [
    37,
    87,
    92,
    104,
    143,
    150,
    224
   ],
   [
    22,
    83,
    88,
    105,
    149,
    188,
    225
   ],
   [
    1,
    39,
    106,
    119,
    145,
    169,
    226
   ],
   [
    1,
    91,
    107,
    115,
    176,
    181,
    227
   ],
   [
    24,
    60,
    92,
    108,
    135,
    222,
    228
   ],
   [
    18,
    43,
    93,
    109,
    136,
    183,
    229
   ],
   [
    12,
    78,
    96,
    110,
    152,
    183,
    230
   ],
   [
    52,
    79,
    97,
    111,
    182,
    198,
    231
   ],
   [
    73,
    80,
    98,
    112,
    140,
    154,
    232
   ],
   [
    17,
    101,
    110,
    113,
    164,
    193,
    233
   ],
   [
    6,
    104,
    108,
    114,
    163,
    171,
    234
   ],
   [
    40,
    42,
    105,
    115,
    170,
    209,
    235
   ],
   [
    7,
    61,
    106,
    116,
    132,
    165,
    236
   ],
   [
    9,
    37,
    109,
    117,
    153,
    204,
    237
   ],
   [
    30,
    99,
    112,
    118,
    159,
    175,
    238
   ],
   [
    20,
    21,
    116,
    119,
    148,
    187,
    239
   ]
  ],
  "Z": [
   [
    0,
    7,
    52,
    120,
    123,
    132,
    198
   ],
   [
    1,
    3,
    64,
    121,
    127,
    226,
    227
   ],
   [
    2,
    35,
    38,
    122,
    125,
    130,
    214
   ],
   [
    3,
    21,
    74,
    123,
    133,
    148,
    155
   ],
   [
    4,
    22,
    30,
    124,
    134,
    149,
    175
   ],
   [
    5,
    76,
    92,
    125,
    135,
    150,
    219
   ],
   [
    6,
    27,
    46,
    126,
    138,
    213,
    234
   ],
   [
    7,
    13,
    85,
    127,
    141,
    190,
    236
   ],
   [
    8,
    14,
    41,
    128,
    142,
    208,
    210
   ],
   [
    9,
    81,
    87,
    129,
    139,
    143,
    237
   ],
   [
    10,
    56,
    60,
    130,
    135,
    146,
    172
   ],
   [
    11,
    17,
    18,
    131,
    136,
    147,
    193
   ],
   [
    12,
    58,
    116,
    132,
    137,
    148,
    230
   ],
   [
    1,
    13,
    94,
    120,
    133,
    169,
    176
   ],
   [
    14,
    42,
    51,
    134,
    137,
    151,
    170
   ],
   [
    15,
    96,
    108,
    135,
    152,
    171,
    178
   ],
   [
    16,
    53,
    109,
    136,
    153,
    172,
    199
   ],
   [
    17,
    69,
    98,
    137,
    154,
    173,
    233
   ],
   [
    18,
    48,
    68,
    138,
    157,
    207,
    229
   ],
   [
    10,
    19,
    25,
    139,
    158,
    191,
    223
   ],
   [
    20,
    70,
    112,
    128,
    140,
    159,
    239
   ],
   [
    0,
    21,
    102,
    121,
    141,
    211,
    239
   ],
   [
    22,
    31,
    63,
    142,
    162,
    167,
    225
   ],
   [
    23,
    100,
    104,
    143,
    158,
    163,
    213
   ],
   [
    24,
    65,
    101,
    126,
    144,
    164,
    228
   ],
   [
    25,
    57,
    106,
    145,
    160,
    162,
    165
   ],
   [
    19,
    26,
    78,
    122,
    146,
    152,
    194
   ],
   [
    27,
    34,
    37,
    147,
    150,
    153,
    168
   ],
   [
    28,
    80,
    119,
    148,
    154,
    169,
    196
   ],
   [
    29,
    36,
    105,
    149,
    155,
    170,
    215
   ],
   [
    30,
    82,
    104,
    150,
    156,
    171,
    238
   ],
   [
    8,
    31,
    73,
    124,
    151,
    154,
    192
   ],
   [
    32,
    71,
    110,
    125,
    152,
    193,
    200
   ],
   [
    33,
    75,
    117,
    153,
    156,
    174,
    194
   ],
   [
    34,
    90,
    112,
    154,
    175,
    195,
    202
   ],
   [
    35,
    77,
    91,
    155,
    176,
    196,
    220
   ],
   [
    11,
    36,
    45,
    151,
    156,
    177,
    197
   ],
   [
    11,
    37,
    89,
    126,
    157,
    224,
    237
   ],
   [
    26,
    38,
    45,
    158,
    180,
    185,
    212
   ],
   [
    39,
    91,
    118,
    142,
    159,
    181,
    226
   ],
   [
    40,
    47,
    97,
    121,
    160,
    182,
    235
   ],
   [
    41,
    93,
    96,
    144,
    161,
    180,
    183
   ],
   [
    4,
    42,
    84,
    128,
    162,
    189,
    235
   ],
   [
    43,
    59,
    114,
    129,
    163,
    180,
    229
   ],
   [
    44,
    86,
    113,
    138,
    164,
    186,
    191
   ],
   [
    45,
    79,
    116,
    128,
    165,
    182,
    187
   ],
   [
    46,
    80,
    88,
    140,
    141,
    166,
    188
   ],
   [
    19,
    34,
    47,
    167,
    184,
    186,
    189
   ],
   [
    6,
    48,
    55,
    131,
    168,
    171,
    174
   ],
   [
    49,
    99,
    106,
    132,
    169,
    175,
    216
   ],
   [
    50,
    57,
    115,
    170,
    173,
    176,
    192
   ],
   [
    51,
    101,
    114,
    171,
    177,
    193,
    218
   ],
   [
    52,
    59,
    86,
    172,
    178,
    194,
    231
   ],
   [
    4,
    53,
    85,
    168,
    173,
    179,
    195
   ],
   [
    54,
    93,
    95,
    136,
    174,
    177,
    214
   ],
   [
    47,
    55,
    118,
    137,
    175,
    215,
    221
   ],
   [
    56,
    97,
    107,
    176,
    179,
    198,
    216
   ],
   [
    27,
    57,
    67,
    124,
    177,
    199,
    217
   ],
   [
    2,
    58,
    68,
    133,
    178,
    200,
    218
   ],
   [
    23,
    29,
    59,
    122,
    174,
    179,
    201
   ],
   [
    2,
    60,
    67,
    139,
    180,
    206,
    228
   ],
   [
    61,
    98,
    107,
    140,
    162,
    181,
    236
   ],
   [
    62,
    69,
    111,
    127,
    182,
    203,
    208
   ],
   [
    63,
    109,
    110,
    139,
    164,
    183,
    204
   ],
   [
    64,
    71,
    75,
    129,
    157,
    184,
    205
   ],
   [
    8,
    65,
    74,
    166,
    185,
    203,
    206
   ],
   [
    66,
    82,
    103,
    144,
    157,
    186,
    212
   ],
   [
    36,
    67,
    119,
    142,
    145,
    187,
    203
   ],
   [
    68,
    99,
    105,
    121,
    159,
    188,
    209
   ],
   [
    38,
    55,
    69,
    144,
    189,
    205,
    210
   ],
   [
    6,
    56,
    70,
    161,
    163,
    190,
    211
   ],
   [
    15,
    40,
    71,
    191,
    207,
    209,
    212
   ],
   [
    72,
    79,
    88,
    149,
    192,
    195,
    198
   ],
   [
    73,
    87,
    113,
    150,
    193,
    199,
    232
   ],
   [
    74,
    81,
    103,
    194,
    197,
    200,
    214
   ],
   [
    14,
    75,
    102,
    131,
    195,
    201,
    215
   ],
   [
    0,
    63,
    76,
    146,
    196,
    202,
    216
   ],
   [
    16,
    62,
    77,
    120,
    192,
    197,
    217
   ],
   [
    70,
    78,
    111,
    155,
    198,
    201,
    230
   ],
   [
    25,
    48,
    79,
    134,
    156,
    199,
    231
   ],
   [
    10,
    80,
    89,
    120,
    200,
    219,
    232
   ],
   [
    43,
    50,
    81,
    130,
    136,
    201,
    220
   ],
   [
    12,
    44,
    82,
    131,
    152,
    202,
    221
   ],
   [
    77,
    83,
    90,
    141,
    160,
    203,
    225
   ],
   [
    76,
    84,
    117,
    158,
    161,
    186,
    204
   ],
   [
    85,
    92,
    95,
    126,
    143,
    205,
    222
   ],
   [
    22,
    86,
    94,
    160,
    188,
    206,
    223
   ],
   [
    1,
    51,
    87,
    145,
    181,
    207,
    224
   ],
   [
    24,
    50,
    88,
    190,
    208,
    222,
    225
   ],
   [
    58,
    89,
    115,
    127,
    166,
    181,
    209
   ],
   [
    17,
    60,
    90,
    164,
    167,
    210,
    222
   ],
   [
    18,
    78,
    91,
    129,
    183,
    211,
    227
   ],
   [
    32,
    62,
    92,
    166,
    212,
    224,
    228
   ],
   [
    20,
    33,
    93,
    185,
    187,
    213,
    229
   ],
   [
    65,
    94,
    100,
    172,
    214,
    217,
    219
   ],
   [
    31,
    64,
    95,
    147,
    173,
    215,
    220
   ],
   [
    3,
    84,
    96,
    122,
    216,
    221,
    230
   ],
   [
    33,
    83,
    97,
    123,
    149,
    217,
    231
   ],
   [
    5,
    39,
    98,
    124,
    169,
    218,
    232
   ],
   [
    26,
    46,
    99,
    123,
    178,
    219,
    238
   ],
   [
    9,
    72,
    100,
    146,
    153,
    179,
    220
   ],
   [
    28,
    66,
    101,
    125,
    147,
    221,
    233
   ],
   [
    53,
    102,
    108,
    138,
    163,
    184,
    222
   ],
   [
    42,
    52,
    103,
    182,
    185,
    209,
    223
   ],
   [
    7,
    73,
    104,
    140,
    165,
    224,
    234
   ],
   [
    44,
    72,
    105,
    184,
    211,
    225,
    235
   ],
   [
    9,
    28,
    106,
    167,
    204,
    226,
    236
   ],
   [
    35,
    37,
    107,
    143,
    190,
    204,
    227
   ],
   [
    5,
    83,
    108,
    188,
    191,
    228,
    234
   ],
   [
    39,
    54,
    109,
    145,
    206,
    229,
    237
   ],
   [
    13,
    41,
    110,
    130,
    196,
    230,
    233
   ],
   [
    40,
    54,
    111,
    133,
    170,
    197,
    231
   ],
   [
    15,
    61,
    112,
    132,
    134,
    232,
    238
   ],
   [
    24,
    49,
    113,
    135,
    168,
    202,
    233
   ],
   [
    21,
    30,
    114,
    159,
    187,
    207,
    234
   ],
   [
    29,
    66,
    115,
    205,
    208,
    227,
    235
   ],
   [
    23,
    49,
    116,
    161,
    189,
    236,
    239
   ],
   [
    16,
    61,
    117,
    165,
    213,
    223,
    237
   ],
   [
    20,
    32,
    118,
    148,
    151,
    218,
    238
   ],
   [
    12,
    43,
    119,
    183,
    210,
    226,
    239
   ]
  ]
 },
 "distance": {
  "d": 18,
  "X": {
   "value": 18,
   "confidence": "upper_bound",
   "witness": [
    5,
    9,
    23,
    28,
    49,
    59,
    86,
    87,
    92,
    94,
    100,
    101,
    113,
    114,
    126,
    169,
    224,
    234
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1002
    ]
   }
  },
  "Z": {
   "value": 18,
   "confidence": "upper_bound",
   "witness": [
    5,
    12,
    14,
    16,
    51,
    54,
    59,
    73,
    94,
    96,
    112,
    118,
    135,
    163,
    171,
    201,
    217,
    228
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1003
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C3 x ((C10 x C2) : C2) = SmallGroup(120, 20) (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, 3, 12, 78}, b = {0, 7, 52} 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"
}