{
 "schema_version": "0.1",
 "name": "[[186,20,18]] two-block code over C93 (Lee, arXiv:2610.13880)",
 "code_type": "CSS",
 "n": 186,
 "k": 20,
 "checks": {
  "X": [
   [
    0,
    14,
    33,
    75,
    85,
    93,
    96,
    127,
    184
   ],
   [
    1,
    16,
    29,
    71,
    87,
    93,
    94,
    129,
    185
   ],
   [
    2,
    17,
    36,
    78,
    88,
    94,
    95,
    99,
    130
   ],
   [
    3,
    18,
    31,
    73,
    83,
    94,
    96,
    125,
    182
   ],
   [
    4,
    19,
    32,
    74,
    90,
    95,
    96,
    97,
    132
   ],
   [
    5,
    20,
    39,
    81,
    91,
    97,
    98,
    102,
    133
   ],
   [
    6,
    21,
    34,
    76,
    86,
    93,
    97,
    99,
    128
   ],
   [
    7,
    22,
    35,
    77,
    92,
    98,
    99,
    100,
    135
   ],
   [
    1,
    8,
    23,
    42,
    84,
    100,
    101,
    105,
    136
   ],
   [
    9,
    24,
    37,
    79,
    89,
    95,
    100,
    102,
    131
   ],
   [
    3,
    10,
    25,
    38,
    80,
    101,
    102,
    103,
    138
   ],
   [
    4,
    11,
    26,
    45,
    87,
    103,
    104,
    108,
    139
   ],
   [
    0,
    12,
    27,
    40,
    82,
    98,
    103,
    105,
    134
   ],
   [
    6,
    13,
    28,
    41,
    83,
    104,
    105,
    106,
    141
   ],
   [
    7,
    14,
    29,
    48,
    90,
    106,
    107,
    111,
    142
   ],
   [
    2,
    15,
    30,
    43,
    85,
    101,
    106,
    108,
    137
   ],
   [
    9,
    16,
    31,
    44,
    86,
    107,
    108,
    109,
    144
   ],
   [
    10,
    17,
    32,
    51,
    92,
    109,
    110,
    114,
    145
   ],
   [
    5,
    18,
    33,
    46,
    88,
    104,
    109,
    111,
    140
   ],
   [
    12,
    19,
    34,
    47,
    89,
    110,
    111,
    112,
    147
   ],
   [
    3,
    13,
    20,
    35,
    54,
    112,
    113,
    117,
    148
   ],
   [
    8,
    21,
    36,
    49,
    91,
    107,
    112,
    114,
    143
   ],
   [
    0,
    15,
    22,
    37,
    50,
    113,
    114,
    115,
    150
   ],
   [
    6,
    16,
    23,
    38,
    57,
    115,
    116,
    120,
    151
   ],
   [
    1,
    11,
    24,
    39,
    52,
    110,
    115,
    117,
    146
   ],
   [
    2,
    18,
    25,
    40,
    53,
    116,
    117,
    118,
    153
   ],
   [
    9,
    19,
    26,
    41,
    60,
    118,
    119,
    123,
    154
   ],
   [
    4,
    14,
    27,
    42,
    55,
    113,
    118,
    120,
    149
   ],
   [
    5,
    21,
    28,
    43,
    56,
    119,
    120,
    121,
    156
   ],
   [
    12,
    22,
    29,
    44,
    63,
    121,
    122,
    126,
    157
   ],
   [
    7,
    17,
    30,
    45,
    58,
    116,
    121,
    123,
    152
   ],
   [
    8,
    24,
    31,
    46,
    59,
    122,
    123,
    124,
    159
   ],
   [
    15,
    25,
    32,
    47,
    66,
    124,
    125,
    129,
    160
   ],
   [
    10,
    20,
    33,
    48,
    61,
    119,
    124,
    126,
    155
   ],
   [
    11,
    27,
    34,
    49,
    62,
    125,
    126,
    127,
    162
   ],
   [
    18,
    28,
    35,
    50,
    69,
    127,
    128,
    132,
    163
   ],
   [
    13,
    23,
    36,
    51,
    64,
    122,
    127,
    129,
    158
   ],
   [
    14,
    30,
    37,
    52,
    65,
    128,
    129,
    130,
    165
   ],
   [
    21,
    31,
    38,
    53,
    72,
    130,
    131,
    135,
    166
   ],
   [
    16,
    26,
    39,
    54,
    67,
    125,
    130,
    132,
    161
   ],
   [
    17,
    33,
    40,
    55,
    68,
    131,
    132,
    133,
    168
   ],
   [
    24,
    34,
    41,
    56,
    75,
    133,
    134,
    138,
    169
   ],
   [
    19,
    29,
    42,
    57,
    70,
    128,
    133,
    135,
    164
   ],
   [
    20,
    36,
    43,
    58,
    71,
    134,
    135,
    136,
    171
   ],
   [
    27,
    37,
    44,
    59,
    78,
    136,
    137,
    141,
    172
   ],
   [
    22,
    32,
    45,
    60,
    73,
    131,
    136,
    138,
    167
   ],
   [
    23,
    39,
    46,
    61,
    74,
    137,
    138,
    139,
    174
   ],
   [
    30,
    40,
    47,
    62,
    81,
    139,
    140,
    144,
    175
   ],
   [
    25,
    35,
    48,
    63,
    76,
    134,
    139,
    141,
    170
   ],
   [
    26,
    42,
    49,
    64,
    77,
    140,
    141,
    142,
    177
   ],
   [
    33,
    43,
    50,
    65,
    84,
    142,
    143,
    147,
    178
   ],
   [
    28,
    38,
    51,
    66,
    79,
    137,
    142,
    144,
    173
   ],
   [
    29,
    45,
    52,
    67,
    80,
    143,
    144,
    145,
    180
   ],
   [
    36,
    46,
    53,
    68,
    87,
    145,
    146,
    150,
    181
   ],
   [
    31,
    41,
    54,
    69,
    82,
    140,
    145,
    147,
    176
   ],
   [
    32,
    48,
    55,
    70,
    83,
    146,
    147,
    148,
    183
   ],
   [
    39,
    49,
    56,
    71,
    90,
    148,
    149,
    153,
    184
   ],
   [
    34,
    44,
    57,
    72,
    85,
    143,
    148,
    150,
    179
   ],
   [
    35,
    51,
    58,
    73,
    86,
    149,
    150,
    151,
    185
   ],
   [
    42,
    52,
    59,
    74,
    92,
    94,
    151,
    152,
    156
   ],
   [
    37,
    47,
    60,
    75,
    88,
    146,
    151,
    153,
    182
   ],
   [
    38,
    54,
    61,
    76,
    89,
    96,
    152,
    153,
    154
   ],
   [
    3,
    45,
    55,
    62,
    77,
    97,
    154,
    155,
    159
   ],
   [
    40,
    50,
    63,
    78,
    91,
    93,
    149,
    154,
    156
   ],
   [
    0,
    41,
    57,
    64,
    79,
    99,
    155,
    156,
    157
   ],
   [
    6,
    48,
    58,
    65,
    80,
    100,
    157,
    158,
    162
   ],
   [
    1,
    43,
    53,
    66,
    81,
    95,
    152,
    157,
    159
   ],
   [
    2,
    44,
    60,
    67,
    82,
    102,
    158,
    159,
    160
   ],
   [
    9,
    51,
    61,
    68,
    83,
    103,
    160,
    161,
    165
   ],
   [
    4,
    46,
    56,
    69,
    84,
    98,
    155,
    160,
    162
   ],
   [
    5,
    47,
    63,
    70,
    85,
    105,
    161,
    162,
    163
   ],
   [
    12,
    54,
    64,
    71,
    86,
    106,
    163,
    164,
    168
   ],
   [
    7,
    49,
    59,
    72,
    87,
    101,
    158,
    163,
    165
   ],
   [
    8,
    50,
    66,
    73,
    88,
    108,
    164,
    165,
    166
   ],
   [
    15,
    57,
    67,
    74,
    89,
    109,
    166,
    167,
    171
   ],
   [
    10,
    52,
    62,
    75,
    90,
    104,
    161,
    166,
    168
   ],
   [
    11,
    53,
    69,
    76,
    91,
    111,
    167,
    168,
    169
   ],
   [
    0,
    18,
    60,
    70,
    77,
    112,
    169,
    170,
    174
   ],
   [
    13,
    55,
    65,
    78,
    92,
    107,
    164,
    169,
    171
   ],
   [
    1,
    14,
    56,
    72,
    79,
    114,
    170,
    171,
    172
   ],
   [
    2,
    21,
    63,
    73,
    80,
    115,
    172,
    173,
    177
   ],
   [
    3,
    16,
    58,
    68,
    81,
    110,
    167,
    172,
    174
   ],
   [
    4,
    17,
    59,
    75,
    82,
    117,
    173,
    174,
    175
   ],
   [
    5,
    24,
    66,
    76,
    83,
    118,
    175,
    176,
    180
   ],
   [
    6,
    19,
    61,
    71,
    84,
    113,
    170,
    175,
    177
   ],
   [
    7,
    20,
    62,
    78,
    85,
    120,
    176,
    177,
    178
   ],
   [
    8,
    27,
    69,
    79,
    86,
    121,
    178,
    179,
    183
   ],
   [
    9,
    22,
    64,
    74,
    87,
    116,
    173,
    178,
    180
   ],
   [
    10,
    23,
    65,
    81,
    88,
    123,
    179,
    180,
    181
   ],
   [
    11,
    30,
    72,
    82,
    89,
    124,
    181,
    182,
    185
   ],
   [
    12,
    25,
    67,
    77,
    90,
    119,
    176,
    181,
    183
   ],
   [
    13,
    26,
    68,
    84,
    91,
    126,
    182,
    183,
    184
   ],
   [
    15,
    28,
    70,
    80,
    92,
    122,
    179,
    184,
    185
   ]
  ],
  "Z": [
   [
    0,
    1,
    6,
    63,
    93,
    105,
    115,
    157,
    170
   ],
   [
    1,
    2,
    3,
    59,
    94,
    101,
    117,
    159,
    172
   ],
   [
    2,
    4,
    9,
    66,
    95,
    108,
    118,
    160,
    173
   ],
   [
    0,
    3,
    4,
    61,
    96,
    103,
    113,
    155,
    174
   ],
   [
    4,
    5,
    6,
    62,
    97,
    104,
    120,
    162,
    175
   ],
   [
    5,
    7,
    12,
    69,
    98,
    111,
    121,
    163,
    176
   ],
   [
    2,
    6,
    7,
    64,
    99,
    106,
    116,
    158,
    177
   ],
   [
    7,
    8,
    9,
    65,
    100,
    107,
    123,
    165,
    178
   ],
   [
    8,
    10,
    15,
    72,
    101,
    114,
    124,
    166,
    179
   ],
   [
    5,
    9,
    10,
    67,
    102,
    109,
    119,
    161,
    180
   ],
   [
    10,
    11,
    12,
    68,
    103,
    110,
    126,
    168,
    181
   ],
   [
    11,
    13,
    18,
    75,
    104,
    117,
    127,
    169,
    182
   ],
   [
    8,
    12,
    13,
    70,
    105,
    112,
    122,
    164,
    183
   ],
   [
    13,
    14,
    15,
    71,
    106,
    113,
    129,
    171,
    184
   ],
   [
    14,
    16,
    21,
    78,
    93,
    107,
    120,
    130,
    172
   ],
   [
    11,
    15,
    16,
    73,
    108,
    115,
    125,
    167,
    185
   ],
   [
    16,
    17,
    18,
    74,
    94,
    109,
    116,
    132,
    174
   ],
   [
    17,
    19,
    24,
    81,
    95,
    110,
    123,
    133,
    175
   ],
   [
    14,
    18,
    19,
    76,
    96,
    111,
    118,
    128,
    170
   ],
   [
    19,
    20,
    21,
    77,
    97,
    112,
    119,
    135,
    177
   ],
   [
    20,
    22,
    27,
    84,
    98,
    113,
    126,
    136,
    178
   ],
   [
    17,
    21,
    22,
    79,
    99,
    114,
    121,
    131,
    173
   ],
   [
    22,
    23,
    24,
    80,
    100,
    115,
    122,
    138,
    180
   ],
   [
    23,
    25,
    30,
    87,
    101,
    116,
    129,
    139,
    181
   ],
   [
    20,
    24,
    25,
    82,
    102,
    117,
    124,
    134,
    176
   ],
   [
    25,
    26,
    27,
    83,
    103,
    118,
    125,
    141,
    183
   ],
   [
    26,
    28,
    33,
    90,
    104,
    119,
    132,
    142,
    184
   ],
   [
    23,
    27,
    28,
    85,
    105,
    120,
    127,
    137,
    179
   ],
   [
    28,
    29,
    30,
    86,
    106,
    121,
    128,
    144,
    185
   ],
   [
    29,
    31,
    36,
    92,
    94,
    107,
    122,
    135,
    145
   ],
   [
    26,
    30,
    31,
    88,
    108,
    123,
    130,
    140,
    182
   ],
   [
    31,
    32,
    33,
    89,
    96,
    109,
    124,
    131,
    147
   ],
   [
    3,
    32,
    34,
    39,
    97,
    110,
    125,
    138,
    148
   ],
   [
    29,
    33,
    34,
    91,
    93,
    111,
    126,
    133,
    143
   ],
   [
    0,
    34,
    35,
    36,
    99,
    112,
    127,
    134,
    150
   ],
   [
    6,
    35,
    37,
    42,
    100,
    113,
    128,
    141,
    151
   ],
   [
    1,
    32,
    36,
    37,
    95,
    114,
    129,
    136,
    146
   ],
   [
    2,
    37,
    38,
    39,
    102,
    115,
    130,
    137,
    153
   ],
   [
    9,
    38,
    40,
    45,
    103,
    116,
    131,
    144,
    154
   ],
   [
    4,
    35,
    39,
    40,
    98,
    117,
    132,
    139,
    149
   ],
   [
    5,
    40,
    41,
    42,
    105,
    118,
    133,
    140,
    156
   ],
   [
    12,
    41,
    43,
    48,
    106,
    119,
    134,
    147,
    157
   ],
   [
    7,
    38,
    42,
    43,
    101,
    120,
    135,
    142,
    152
   ],
   [
    8,
    43,
    44,
    45,
    108,
    121,
    136,
    143,
    159
   ],
   [
    15,
    44,
    46,
    51,
    109,
    122,
    137,
    150,
    160
   ],
   [
    10,
    41,
    45,
    46,
    104,
    123,
    138,
    145,
    155
   ],
   [
    11,
    46,
    47,
    48,
    111,
    124,
    139,
    146,
    162
   ],
   [
    18,
    47,
    49,
    54,
    112,
    125,
    140,
    153,
    163
   ],
   [
    13,
    44,
    48,
    49,
    107,
    126,
    141,
    148,
    158
   ],
   [
    14,
    49,
    50,
    51,
    114,
    127,
    142,
    149,
    165
   ],
   [
    21,
    50,
    52,
    57,
    115,
    128,
    143,
    156,
    166
   ],
   [
    16,
    47,
    51,
    52,
    110,
    129,
    144,
    151,
    161
   ],
   [
    17,
    52,
    53,
    54,
    117,
    130,
    145,
    152,
    168
   ],
   [
    24,
    53,
    55,
    60,
    118,
    131,
    146,
    159,
    169
   ],
   [
    19,
    50,
    54,
    55,
    113,
    132,
    147,
    154,
    164
   ],
   [
    20,
    55,
    56,
    57,
    120,
    133,
    148,
    155,
    171
   ],
   [
    27,
    56,
    58,
    63,
    121,
    134,
    149,
    162,
    172
   ],
   [
    22,
    53,
    57,
    58,
    116,
    135,
    150,
    157,
    167
   ],
   [
    23,
    58,
    59,
    60,
    123,
    136,
    151,
    158,
    174
   ],
   [
    30,
    59,
    61,
    66,
    124,
    137,
    152,
    165,
    175
   ],
   [
    25,
    56,
    60,
    61,
    119,
    138,
    153,
    160,
    170
   ],
   [
    26,
    61,
    62,
    63,
    126,
    139,
    154,
    161,
    177
   ],
   [
    33,
    62,
    64,
    69,
    127,
    140,
    155,
    168,
    178
   ],
   [
    28,
    59,
    63,
    64,
    122,
    141,
    156,
    163,
    173
   ],
   [
    29,
    64,
    65,
    66,
    129,
    142,
    157,
    164,
    180
   ],
   [
    36,
    65,
    67,
    72,
    130,
    143,
    158,
    171,
    181
   ],
   [
    31,
    62,
    66,
    67,
    125,
    144,
    159,
    166,
    176
   ],
   [
    32,
    67,
    68,
    69,
    132,
    145,
    160,
    167,
    183
   ],
   [
    39,
    68,
    70,
    75,
    133,
    146,
    161,
    174,
    184
   ],
   [
    34,
    65,
    69,
    70,
    128,
    147,
    162,
    169,
    179
   ],
   [
    35,
    70,
    71,
    72,
    135,
    148,
    163,
    170,
    185
   ],
   [
    42,
    71,
    73,
    78,
    94,
    136,
    149,
    164,
    177
   ],
   [
    37,
    68,
    72,
    73,
    131,
    150,
    165,
    172,
    182
   ],
   [
    38,
    73,
    74,
    75,
    96,
    138,
    151,
    166,
    173
   ],
   [
    45,
    74,
    76,
    81,
    97,
    139,
    152,
    167,
    180
   ],
   [
    40,
    71,
    75,
    76,
    93,
    134,
    153,
    168,
    175
   ],
   [
    41,
    76,
    77,
    78,
    99,
    141,
    154,
    169,
    176
   ],
   [
    48,
    77,
    79,
    84,
    100,
    142,
    155,
    170,
    183
   ],
   [
    43,
    74,
    78,
    79,
    95,
    137,
    156,
    171,
    178
   ],
   [
    44,
    79,
    80,
    81,
    102,
    144,
    157,
    172,
    179
   ],
   [
    51,
    80,
    82,
    87,
    103,
    145,
    158,
    173,
    185
   ],
   [
    46,
    77,
    81,
    82,
    98,
    140,
    159,
    174,
    181
   ],
   [
    47,
    82,
    83,
    84,
    105,
    147,
    160,
    175,
    182
   ],
   [
    54,
    83,
    85,
    90,
    96,
    106,
    148,
    161,
    176
   ],
   [
    49,
    80,
    84,
    85,
    101,
    143,
    162,
    177,
    184
   ],
   [
    50,
    85,
    86,
    87,
    93,
    108,
    150,
    163,
    178
   ],
   [
    57,
    86,
    88,
    92,
    99,
    109,
    151,
    164,
    179
   ],
   [
    52,
    83,
    87,
    88,
    94,
    104,
    146,
    165,
    180
   ],
   [
    53,
    88,
    89,
    90,
    95,
    111,
    153,
    166,
    181
   ],
   [
    3,
    60,
    89,
    91,
    102,
    112,
    154,
    167,
    182
   ],
   [
    55,
    86,
    90,
    91,
    97,
    107,
    149,
    168,
    183
   ],
   [
    0,
    56,
    91,
    92,
    98,
    114,
    156,
    169,
    184
   ],
   [
    1,
    58,
    89,
    92,
    100,
    110,
    152,
    171,
    185
   ]
  ]
 },
 "distance": {
  "d": 18,
  "X": {
   "value": 18,
   "confidence": "upper_bound",
   "witness": [
    2,
    5,
    14,
    18,
    26,
    49,
    55,
    67,
    71,
    76,
    97,
    117,
    118,
    130,
    132,
    148,
    176,
    177
   ]
  },
  "Z": {
   "value": 18,
   "confidence": "upper_bound",
   "witness": [
    17,
    35,
    39,
    47,
    54,
    68,
    82,
    87,
    94,
    98,
    110,
    116,
    139,
    151,
    153,
    160,
    163,
    182
   ]
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) of arXiv:2610.13880 (Tables 2 and 11) over the cyclic group C93 (GAP SmallGroup(93,2)): 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 = 1 + x^7 + x^52 + x^57 + x^65, b = 1 + x^20 + x^31 + x^32 in a generator x of order 93, i.e. the generalized bicycle code with A = a(x), B = b(x). The stored matrices use the qubit ordering of the paper's database (record acb02b92594b75a4, github.com/gideonlsx/bicycle-race @ aed705a, data/codes.jsonl, CC BY 4.0): qubits 0..92 are the left block and 93..185 the right block, group elements numbered as GAP's Elements(SmallGroup(93,2)) with e0 the identity, x = e4, so a = e0 + e12 + e22 + e64 + e77, b = e0 + e1 + e6 + e63. 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: equal to d_Z by a checked X/Z-exchange automorphism; d_Z: ladder (cluster engine, symmetry roots), from the screen's lower bound 17, no target; verification record: checked: GAP rebuild, QDistRnd and QDistEvol find nothing below d). 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/186-20-18.md.",
  "novelty": "known_parameters",
  "references": [
   "arXiv:2610.13880"
  ]
 },
 "family": "generalized-bicycle"
}