{
 "schema_version": "0.1",
 "name": "[[240,4,18]] two-block code over C5 x (C3 : C8) (Lee, arXiv:2610.13880)",
 "code_type": "CSS",
 "n": 240,
 "k": 4,
 "checks": {
  "X": [
   [
    0,
    59,
    102,
    120,
    214
   ],
   [
    1,
    45,
    48,
    121,
    222
   ],
   [
    2,
    22,
    82,
    122,
    134
   ],
   [
    3,
    17,
    60,
    123,
    168
   ],
   [
    4,
    35,
    83,
    124,
    192
   ],
   [
    5,
    14,
    114,
    125,
    230
   ],
   [
    0,
    6,
    68,
    126,
    142
   ],
   [
    7,
    9,
    72,
    127,
    180
   ],
   [
    8,
    23,
    73,
    128,
    203
   ],
   [
    9,
    71,
    74,
    129,
    234
   ],
   [
    10,
    41,
    101,
    130,
    150
   ],
   [
    1,
    11,
    33,
    120,
    131
   ],
   [
    7,
    12,
    57,
    123,
    132
   ],
   [
    13,
    30,
    45,
    133,
    154
   ],
   [
    14,
    36,
    84,
    134,
    193
   ],
   [
    0,
    15,
    85,
    135,
    194
   ],
   [
    3,
    16,
    103,
    136,
    215
   ],
   [
    17,
    34,
    119,
    137,
    238
   ],
   [
    2,
    18,
    90,
    138,
    161
   ],
   [
    3,
    19,
    21,
    121,
    139
   ],
   [
    4,
    20,
    42,
    127,
    140
   ],
   [
    5,
    21,
    93,
    141,
    165
   ],
   [
    22,
    24,
    94,
    142,
    204
   ],
   [
    23,
    25,
    95,
    143,
    205
   ],
   [
    24,
    46,
    96,
    144,
    223
   ],
   [
    22,
    25,
    97,
    145,
    239
   ],
   [
    26,
    64,
    113,
    146,
    172
   ],
   [
    6,
    27,
    55,
    122,
    147
   ],
   [
    19,
    28,
    80,
    131,
    148
   ],
   [
    29,
    52,
    68,
    149,
    176
   ],
   [
    8,
    30,
    58,
    124,
    150
   ],
   [
    2,
    9,
    31,
    125,
    151
   ],
   [
    11,
    23,
    32,
    135,
    152
   ],
   [
    33,
    56,
    71,
    153,
    179
   ],
   [
    4,
    34,
    104,
    154,
    216
   ],
   [
    5,
    35,
    105,
    155,
    217
   ],
   [
    15,
    36,
    115,
    156,
    231
   ],
   [
    10,
    37,
    106,
    157,
    184
   ],
   [
    11,
    38,
    40,
    126,
    158
   ],
   [
    12,
    39,
    65,
    139,
    159
   ],
   [
    13,
    40,
    109,
    160,
    188
   ],
   [
    14,
    41,
    43,
    128,
    161
   ],
   [
    15,
    42,
    44,
    129,
    162
   ],
   [
    16,
    43,
    69,
    143,
    163
   ],
   [
    17,
    41,
    44,
    164,
    191
   ],
   [
    45,
    47,
    110,
    165,
    224
   ],
   [
    1,
    46,
    111,
    166,
    225
   ],
   [
    7,
    47,
    112,
    167,
    235
   ],
   [
    48,
    86,
    118,
    168,
    195
   ],
   [
    18,
    49,
    78,
    130,
    169
   ],
   [
    38,
    50,
    99,
    147,
    170
   ],
   [
    51,
    75,
    90,
    171,
    199
   ],
   [
    20,
    52,
    81,
    132,
    172
   ],
   [
    10,
    21,
    53,
    133,
    173
   ],
   [
    27,
    42,
    54,
    151,
    174
   ],
   [
    55,
    79,
    93,
    175,
    202
   ],
   [
    12,
    24,
    56,
    136,
    176
   ],
   [
    13,
    25,
    57,
    137,
    177
   ],
   [
    31,
    46,
    58,
    155,
    178
   ],
   [
    16,
    59,
    116,
    179,
    232
   ],
   [
    26,
    60,
    114,
    180,
    206
   ],
   [
    27,
    61,
    63,
    138,
    181
   ],
   [
    28,
    62,
    87,
    158,
    182
   ],
   [
    29,
    63,
    117,
    183,
    210
   ],
   [
    30,
    64,
    66,
    140,
    184
   ],
   [
    31,
    65,
    67,
    141,
    185
   ],
   [
    32,
    66,
    91,
    162,
    186
   ],
   [
    33,
    64,
    67,
    187,
    213
   ],
   [
    34,
    68,
    70,
    144,
    188
   ],
   [
    6,
    35,
    69,
    145,
    189
   ],
   [
    19,
    36,
    70,
    166,
    190
   ],
   [
    8,
    71,
    118,
    191,
    236
   ],
   [
    37,
    72,
    97,
    146,
    192
   ],
   [
    61,
    73,
    111,
    169,
    193
   ],
   [
    74,
    94,
    106,
    194,
    218
   ],
   [
    39,
    75,
    100,
    148,
    195
   ],
   [
    26,
    40,
    76,
    149,
    196
   ],
   [
    49,
    65,
    77,
    173,
    197
   ],
   [
    78,
    98,
    109,
    198,
    221
   ],
   [
    28,
    43,
    79,
    152,
    199
   ],
   [
    29,
    44,
    80,
    153,
    200
   ],
   [
    53,
    69,
    81,
    177,
    201
   ],
   [
    32,
    47,
    82,
    156,
    202
   ],
   [
    49,
    83,
    85,
    157,
    203
   ],
   [
    50,
    84,
    103,
    181,
    204
   ],
   [
    51,
    85,
    119,
    205,
    226
   ],
   [
    52,
    86,
    88,
    159,
    206
   ],
   [
    53,
    87,
    89,
    160,
    207
   ],
   [
    54,
    88,
    107,
    185,
    208
   ],
   [
    55,
    86,
    89,
    209,
    229
   ],
   [
    56,
    90,
    92,
    163,
    210
   ],
   [
    18,
    57,
    91,
    164,
    211
   ],
   [
    38,
    58,
    92,
    189,
    212
   ],
   [
    20,
    59,
    93,
    167,
    213
   ],
   [
    62,
    94,
    112,
    170,
    214
   ],
   [
    48,
    63,
    95,
    171,
    215
   ],
   [
    72,
    87,
    96,
    196,
    216
   ],
   [
    97,
    110,
    117,
    217,
    233
   ],
   [
    50,
    66,
    98,
    174,
    218
   ],
   [
    51,
    67,
    99,
    175,
    219
   ],
   [
    76,
    91,
    100,
    200,
    220
   ],
   [
    54,
    70,
    101,
    178,
    221
   ],
   [
    75,
    102,
    104,
    182,
    222
   ],
   [
    76,
    103,
    105,
    183,
    223
   ],
   [
    77,
    104,
    115,
    207,
    224
   ],
   [
    78,
    102,
    105,
    225,
    237
   ],
   [
    79,
    106,
    108,
    186,
    226
   ],
   [
    37,
    80,
    107,
    187,
    227
   ],
   [
    61,
    81,
    108,
    211,
    228
   ],
   [
    39,
    82,
    109,
    190,
    229
   ],
   [
    73,
    88,
    110,
    197,
    230
   ],
   [
    74,
    89,
    111,
    198,
    231
   ],
   [
    95,
    107,
    112,
    219,
    232
   ],
   [
    77,
    92,
    113,
    201,
    233
   ],
   [
    98,
    114,
    116,
    208,
    234
   ],
   [
    60,
    99,
    115,
    209,
    235
   ],
   [
    83,
    100,
    116,
    227,
    236
   ],
   [
    62,
    101,
    117,
    212,
    237
   ],
   [
    96,
    108,
    118,
    220,
    238
   ],
   [
    84,
    113,
    119,
    228,
    239
   ]
  ],
  "Z": [
   [
    0,
    11,
    120,
    126,
    135
   ],
   [
    1,
    19,
    121,
    131,
    166
   ],
   [
    2,
    27,
    122,
    138,
    151
   ],
   [
    3,
    12,
    123,
    136,
    139
   ],
   [
    4,
    30,
    124,
    140,
    154
   ],
   [
    5,
    31,
    125,
    141,
    155
   ],
   [
    6,
    38,
    126,
    147,
    189
   ],
   [
    7,
    20,
    127,
    132,
    167
   ],
   [
    8,
    41,
    128,
    150,
    191
   ],
   [
    9,
    42,
    127,
    129,
    151
   ],
   [
    10,
    49,
    130,
    157,
    173
   ],
   [
    11,
    28,
    131,
    152,
    158
   ],
   [
    12,
    52,
    132,
    159,
    176
   ],
   [
    13,
    53,
    133,
    160,
    177
   ],
   [
    2,
    14,
    125,
    134,
    161
   ],
   [
    15,
    32,
    135,
    156,
    162
   ],
   [
    16,
    56,
    136,
    163,
    179
   ],
   [
    17,
    57,
    123,
    137,
    164
   ],
   [
    18,
    61,
    138,
    169,
    211
   ],
   [
    19,
    39,
    139,
    148,
    190
   ],
   [
    20,
    64,
    140,
    172,
    213
   ],
   [
    21,
    65,
    139,
    141,
    173
   ],
   [
    6,
    22,
    122,
    142,
    145
   ],
   [
    23,
    43,
    128,
    143,
    152
   ],
   [
    24,
    68,
    142,
    144,
    176
   ],
   [
    25,
    69,
    143,
    145,
    177
   ],
   [
    26,
    72,
    146,
    180,
    196
   ],
   [
    27,
    50,
    147,
    174,
    181
   ],
   [
    28,
    75,
    148,
    182,
    199
   ],
   [
    29,
    76,
    149,
    183,
    200
   ],
   [
    10,
    30,
    133,
    150,
    184
   ],
   [
    31,
    54,
    151,
    178,
    185
   ],
   [
    32,
    79,
    152,
    186,
    202
   ],
   [
    33,
    80,
    131,
    153,
    187
   ],
   [
    13,
    34,
    137,
    154,
    188
   ],
   [
    35,
    58,
    124,
    155,
    189
   ],
   [
    36,
    82,
    134,
    156,
    190
   ],
   [
    37,
    83,
    157,
    192,
    227
   ],
   [
    38,
    62,
    158,
    170,
    212
   ],
   [
    39,
    86,
    159,
    195,
    229
   ],
   [
    40,
    87,
    158,
    160,
    196
   ],
   [
    18,
    41,
    130,
    161,
    164
   ],
   [
    42,
    66,
    140,
    162,
    174
   ],
   [
    43,
    90,
    161,
    163,
    199
   ],
   [
    44,
    91,
    162,
    164,
    200
   ],
   [
    21,
    45,
    121,
    133,
    165
   ],
   [
    46,
    70,
    144,
    166,
    178
   ],
   [
    47,
    93,
    165,
    167,
    202
   ],
   [
    3,
    48,
    121,
    168,
    215
   ],
   [
    49,
    73,
    169,
    197,
    203
   ],
   [
    50,
    94,
    170,
    204,
    218
   ],
   [
    51,
    95,
    171,
    205,
    219
   ],
   [
    26,
    52,
    149,
    172,
    206
   ],
   [
    53,
    77,
    173,
    201,
    207
   ],
   [
    54,
    98,
    174,
    208,
    221
   ],
   [
    55,
    99,
    147,
    175,
    209
   ],
   [
    29,
    56,
    153,
    176,
    210
   ],
   [
    57,
    81,
    132,
    177,
    211
   ],
   [
    58,
    101,
    150,
    178,
    212
   ],
   [
    33,
    59,
    120,
    179,
    213
   ],
   [
    7,
    60,
    123,
    180,
    235
   ],
   [
    61,
    84,
    181,
    193,
    228
   ],
   [
    62,
    102,
    182,
    214,
    237
   ],
   [
    63,
    103,
    181,
    183,
    215
   ],
   [
    37,
    64,
    146,
    184,
    187
   ],
   [
    65,
    88,
    159,
    185,
    197
   ],
   [
    66,
    106,
    184,
    186,
    218
   ],
   [
    67,
    107,
    185,
    187,
    219
   ],
   [
    40,
    68,
    126,
    149,
    188
   ],
   [
    69,
    92,
    163,
    189,
    201
   ],
   [
    70,
    109,
    188,
    190,
    221
   ],
   [
    44,
    71,
    129,
    153,
    191
   ],
   [
    4,
    72,
    127,
    192,
    216
   ],
   [
    14,
    73,
    128,
    193,
    230
   ],
   [
    15,
    74,
    129,
    194,
    231
   ],
   [
    48,
    75,
    171,
    195,
    222
   ],
   [
    76,
    96,
    196,
    220,
    223
   ],
   [
    77,
    110,
    197,
    224,
    233
   ],
   [
    78,
    111,
    169,
    198,
    225
   ],
   [
    51,
    79,
    175,
    199,
    226
   ],
   [
    80,
    100,
    148,
    200,
    227
   ],
   [
    81,
    113,
    172,
    201,
    228
   ],
   [
    55,
    82,
    122,
    202,
    229
   ],
   [
    8,
    83,
    124,
    203,
    236
   ],
   [
    22,
    84,
    134,
    204,
    239
   ],
   [
    23,
    85,
    135,
    203,
    205
   ],
   [
    60,
    86,
    168,
    206,
    209
   ],
   [
    87,
    104,
    182,
    207,
    216
   ],
   [
    88,
    114,
    206,
    208,
    230
   ],
   [
    89,
    115,
    207,
    209,
    231
   ],
   [
    63,
    90,
    138,
    171,
    210
   ],
   [
    91,
    108,
    186,
    211,
    220
   ],
   [
    92,
    117,
    210,
    212,
    233
   ],
   [
    67,
    93,
    141,
    175,
    213
   ],
   [
    0,
    94,
    142,
    194,
    214
   ],
   [
    16,
    95,
    143,
    215,
    232
   ],
   [
    34,
    96,
    144,
    216,
    238
   ],
   [
    35,
    97,
    145,
    192,
    217
   ],
   [
    74,
    98,
    198,
    218,
    234
   ],
   [
    99,
    112,
    170,
    219,
    235
   ],
   [
    100,
    118,
    195,
    220,
    236
   ],
   [
    78,
    101,
    130,
    221,
    237
   ],
   [
    1,
    102,
    120,
    222,
    225
   ],
   [
    24,
    103,
    136,
    204,
    223
   ],
   [
    45,
    104,
    154,
    222,
    224
   ],
   [
    46,
    105,
    155,
    223,
    225
   ],
   [
    85,
    106,
    157,
    194,
    226
   ],
   [
    107,
    116,
    208,
    227,
    232
   ],
   [
    108,
    119,
    226,
    228,
    238
   ],
   [
    89,
    109,
    160,
    198,
    229
   ],
   [
    5,
    110,
    165,
    217,
    230
   ],
   [
    36,
    111,
    166,
    193,
    231
   ],
   [
    59,
    112,
    167,
    214,
    232
   ],
   [
    97,
    113,
    146,
    233,
    239
   ],
   [
    9,
    114,
    125,
    180,
    234
   ],
   [
    47,
    115,
    156,
    224,
    235
   ],
   [
    71,
    116,
    179,
    234,
    236
   ],
   [
    105,
    117,
    183,
    217,
    237
   ],
   [
    17,
    118,
    168,
    191,
    238
   ],
   [
    25,
    119,
    137,
    205,
    239
   ]
  ]
 },
 "distance": {
  "d": 18,
  "X": {
   "value": 18,
   "confidence": "upper_bound",
   "witness": [
    37,
    51,
    63,
    64,
    66,
    86,
    100,
    106,
    171,
    172,
    174,
    181,
    195,
    206,
    208,
    226,
    227,
    228
   ]
  },
  "Z": {
   "value": 18,
   "confidence": "upper_bound",
   "witness": [
    4,
    6,
    20,
    21,
    35,
    52,
    55,
    68,
    70,
    93,
    133,
    139,
    154,
    155,
    159,
    178,
    190,
    229
   ]
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) of arXiv:2610.13880 (Sec. 3) over the non-abelian group C5 x (C3 : C8) (GAP SmallGroup(120,1), order 120): H_X = (L(a) | R(b)), H_Z = (R(b)^T | L(a)^T) with L and R the left and right regular representations, a = e0 + e6 + e15, b = e0 + e11 with elements numbered as GAP's Elements(SmallGroup(120,1)), e0 the identity. Taken from record 5859f45864653ece of the paper's database (github.com/gideonlsx/bicycle-race @ aed705a, data/codes.jsonl, CC BY 4.0), whose data/groups.jsonl gives the generators' right-multiplication permutations in that numbering; qubits 0..119 are the left block and 120..239 the right block. Rebuilt from the database's group data; CSS commutation, k, check weight and both of the paper's witnesses were re-checked on the rebuilt matrices.",
  "origin": "baseline",
  "date": "2026-10-12",
  "model": "Claude Fable 5.1 (Claude Code)",
  "notes": "Literature reconstruction. The paper states d = 18 exactly (d_X: ladder (cluster engine, default plan), no target; d_Z: ladder (cluster engine, default plan), no target; verification record: new (beats cited [[192,4,16]], 5.33)). Readings here: qldpc submit's RIS (20,000 NumPy trials per side) and its 2,000,000-trial accelerator pass, plus the verifier's refutation search; witnessed upper bound, see notes/240-4-18.md.",
  "novelty": "known_parameters",
  "references": [
   "arXiv:2610.13880"
  ]
 },
 "family": "generalized-bicycle"
}
