{
 "schema_version": "0.1",
 "name": "[[186,10,14]] twisted-torus BB code (arXiv:2503.03827)",
 "code_type": "CSS",
 "n": 186,
 "k": 10,
 "checks": {
  "X": [
   [
    0,
    1,
    18,
    93,
    95,
    153
   ],
   [
    1,
    3,
    24,
    94,
    97,
    162
   ],
   [
    2,
    4,
    25,
    95,
    98,
    163
   ],
   [
    3,
    6,
    31,
    96,
    100,
    169
   ],
   [
    4,
    7,
    32,
    97,
    101,
    170
   ],
   [
    5,
    8,
    33,
    96,
    98,
    102
   ],
   [
    6,
    10,
    39,
    99,
    104,
    174
   ],
   [
    7,
    11,
    40,
    100,
    105,
    175
   ],
   [
    8,
    12,
    41,
    99,
    101,
    106
   ],
   [
    9,
    13,
    42,
    100,
    102,
    107
   ],
   [
    10,
    15,
    48,
    103,
    109,
    178
   ],
   [
    11,
    16,
    49,
    104,
    110,
    179
   ],
   [
    12,
    17,
    50,
    103,
    105,
    111
   ],
   [
    13,
    18,
    51,
    104,
    106,
    112
   ],
   [
    14,
    19,
    52,
    105,
    107,
    113
   ],
   [
    15,
    21,
    58,
    108,
    115,
    181
   ],
   [
    16,
    22,
    59,
    109,
    116,
    182
   ],
   [
    17,
    23,
    60,
    108,
    110,
    117
   ],
   [
    18,
    24,
    61,
    109,
    111,
    118
   ],
   [
    0,
    19,
    25,
    110,
    112,
    119
   ],
   [
    20,
    26,
    62,
    111,
    113,
    120
   ],
   [
    21,
    28,
    67,
    114,
    122,
    183
   ],
   [
    22,
    29,
    68,
    115,
    123,
    184
   ],
   [
    23,
    30,
    69,
    114,
    116,
    124
   ],
   [
    24,
    31,
    70,
    115,
    117,
    125
   ],
   [
    1,
    25,
    32,
    116,
    118,
    126
   ],
   [
    2,
    26,
    33,
    117,
    119,
    127
   ],
   [
    27,
    34,
    71,
    118,
    120,
    128
   ],
   [
    28,
    36,
    74,
    121,
    130,
    137
   ],
   [
    29,
    37,
    75,
    122,
    131,
    185
   ],
   [
    30,
    38,
    76,
    121,
    123,
    132
   ],
   [
    31,
    39,
    77,
    122,
    124,
    133
   ],
   [
    3,
    32,
    40,
    123,
    125,
    134
   ],
   [
    4,
    33,
    41,
    124,
    126,
    135
   ],
   [
    5,
    34,
    42,
    125,
    127,
    136
   ],
   [
    35,
    43,
    64,
    126,
    128,
    137
   ],
   [
    36,
    45,
    79,
    129,
    139,
    146
   ],
   [
    37,
    46,
    80,
    130,
    140,
    147
   ],
   [
    38,
    47,
    81,
    129,
    131,
    141
   ],
   [
    39,
    48,
    82,
    130,
    132,
    142
   ],
   [
    6,
    40,
    49,
    131,
    133,
    143
   ],
   [
    7,
    41,
    50,
    132,
    134,
    144
   ],
   [
    8,
    42,
    51,
    133,
    135,
    145
   ],
   [
    9,
    43,
    52,
    134,
    136,
    146
   ],
   [
    44,
    53,
    72,
    135,
    137,
    147
   ],
   [
    45,
    55,
    83,
    138,
    149,
    155
   ],
   [
    46,
    56,
    84,
    139,
    150,
    156
   ],
   [
    47,
    57,
    85,
    138,
    140,
    151
   ],
   [
    48,
    58,
    86,
    139,
    141,
    152
   ],
   [
    10,
    49,
    59,
    140,
    142,
    153
   ],
   [
    11,
    50,
    60,
    141,
    143,
    154
   ],
   [
    12,
    51,
    61,
    93,
    142,
    144
   ],
   [
    0,
    13,
    52,
    143,
    145,
    155
   ],
   [
    14,
    53,
    62,
    144,
    146,
    156
   ],
   [
    54,
    63,
    78,
    138,
    145,
    147
   ],
   [
    27,
    55,
    64,
    95,
    148,
    158
   ],
   [
    56,
    65,
    87,
    149,
    159,
    164
   ],
   [
    57,
    66,
    88,
    148,
    150,
    160
   ],
   [
    58,
    67,
    89,
    149,
    151,
    161
   ],
   [
    15,
    59,
    68,
    150,
    152,
    162
   ],
   [
    16,
    60,
    69,
    151,
    153,
    163
   ],
   [
    17,
    61,
    70,
    94,
    152,
    154
   ],
   [
    2,
    19,
    62,
    154,
    155,
    164
   ],
   [
    20,
    63,
    71,
    93,
    148,
    156
   ],
   [
    9,
    34,
    64,
    97,
    157,
    165
   ],
   [
    35,
    65,
    72,
    98,
    158,
    166
   ],
   [
    66,
    73,
    90,
    157,
    159,
    167
   ],
   [
    67,
    74,
    91,
    158,
    160,
    168
   ],
   [
    21,
    68,
    75,
    159,
    161,
    169
   ],
   [
    22,
    69,
    76,
    160,
    162,
    170
   ],
   [
    23,
    70,
    77,
    96,
    161,
    163
   ],
   [
    5,
    26,
    71,
    94,
    157,
    164
   ],
   [
    14,
    43,
    72,
    101,
    165,
    171
   ],
   [
    44,
    73,
    78,
    102,
    166,
    172
   ],
   [
    74,
    79,
    92,
    165,
    167,
    173
   ],
   [
    28,
    75,
    80,
    166,
    168,
    174
   ],
   [
    29,
    76,
    81,
    167,
    169,
    175
   ],
   [
    30,
    77,
    82,
    99,
    168,
    170
   ],
   [
    20,
    53,
    78,
    106,
    171,
    176
   ],
   [
    54,
    79,
    83,
    107,
    172,
    177
   ],
   [
    36,
    80,
    84,
    171,
    173,
    178
   ],
   [
    37,
    81,
    85,
    172,
    174,
    179
   ],
   [
    38,
    82,
    86,
    103,
    173,
    175
   ],
   [
    27,
    63,
    83,
    112,
    176,
    180
   ],
   [
    45,
    84,
    87,
    113,
    177,
    181
   ],
   [
    46,
    85,
    88,
    176,
    178,
    182
   ],
   [
    47,
    86,
    89,
    108,
    177,
    179
   ],
   [
    35,
    55,
    87,
    119,
    180,
    183
   ],
   [
    56,
    88,
    90,
    120,
    181,
    184
   ],
   [
    57,
    89,
    91,
    114,
    180,
    182
   ],
   [
    44,
    65,
    90,
    127,
    183,
    185
   ],
   [
    66,
    91,
    92,
    121,
    128,
    184
   ],
   [
    54,
    73,
    92,
    129,
    136,
    185
   ]
  ],
  "Z": [
   [
    0,
    51,
    63,
    93,
    112,
    145
   ],
   [
    1,
    61,
    71,
    93,
    94,
    118
   ],
   [
    0,
    2,
    55,
    95,
    119,
    155
   ],
   [
    3,
    5,
    70,
    94,
    96,
    125
   ],
   [
    1,
    4,
    64,
    95,
    97,
    126
   ],
   [
    2,
    5,
    65,
    98,
    127,
    164
   ],
   [
    6,
    8,
    77,
    96,
    99,
    133
   ],
   [
    3,
    7,
    9,
    97,
    100,
    134
   ],
   [
    4,
    8,
    72,
    98,
    101,
    135
   ],
   [
    5,
    9,
    73,
    102,
    136,
    157
   ],
   [
    10,
    12,
    82,
    99,
    103,
    142
   ],
   [
    6,
    11,
    13,
    100,
    104,
    143
   ],
   [
    7,
    12,
    14,
    101,
    105,
    144
   ],
   [
    8,
    13,
    78,
    102,
    106,
    145
   ],
   [
    9,
    14,
    79,
    107,
    146,
    165
   ],
   [
    15,
    17,
    86,
    103,
    108,
    152
   ],
   [
    10,
    16,
    18,
    104,
    109,
    153
   ],
   [
    11,
    17,
    19,
    105,
    110,
    154
   ],
   [
    12,
    18,
    20,
    93,
    106,
    111
   ],
   [
    13,
    19,
    83,
    107,
    112,
    155
   ],
   [
    14,
    20,
    84,
    113,
    156,
    171
   ],
   [
    21,
    23,
    89,
    108,
    114,
    161
   ],
   [
    15,
    22,
    24,
    109,
    115,
    162
   ],
   [
    16,
    23,
    25,
    110,
    116,
    163
   ],
   [
    17,
    24,
    26,
    94,
    111,
    117
   ],
   [
    18,
    25,
    27,
    95,
    112,
    118
   ],
   [
    19,
    26,
    87,
    113,
    119,
    164
   ],
   [
    20,
    27,
    88,
    120,
    148,
    176
   ],
   [
    28,
    30,
    91,
    114,
    121,
    168
   ],
   [
    21,
    29,
    31,
    115,
    122,
    169
   ],
   [
    22,
    30,
    32,
    116,
    123,
    170
   ],
   [
    23,
    31,
    33,
    96,
    117,
    124
   ],
   [
    24,
    32,
    34,
    97,
    118,
    125
   ],
   [
    25,
    33,
    35,
    98,
    119,
    126
   ],
   [
    26,
    34,
    90,
    120,
    127,
    157
   ],
   [
    27,
    35,
    91,
    128,
    158,
    180
   ],
   [
    36,
    38,
    92,
    121,
    129,
    173
   ],
   [
    28,
    37,
    39,
    122,
    130,
    174
   ],
   [
    29,
    38,
    40,
    123,
    131,
    175
   ],
   [
    30,
    39,
    41,
    99,
    124,
    132
   ],
   [
    31,
    40,
    42,
    100,
    125,
    133
   ],
   [
    32,
    41,
    43,
    101,
    126,
    134
   ],
   [
    33,
    42,
    44,
    102,
    127,
    135
   ],
   [
    34,
    43,
    92,
    128,
    136,
    165
   ],
   [
    28,
    35,
    44,
    137,
    166,
    183
   ],
   [
    45,
    47,
    54,
    129,
    138,
    177
   ],
   [
    36,
    46,
    48,
    130,
    139,
    178
   ],
   [
    37,
    47,
    49,
    131,
    140,
    179
   ],
   [
    38,
    48,
    50,
    103,
    132,
    141
   ],
   [
    39,
    49,
    51,
    104,
    133,
    142
   ],
   [
    40,
    50,
    52,
    105,
    134,
    143
   ],
   [
    41,
    51,
    53,
    106,
    135,
    144
   ],
   [
    42,
    52,
    54,
    107,
    136,
    145
   ],
   [
    36,
    43,
    53,
    137,
    146,
    171
   ],
   [
    37,
    44,
    54,
    147,
    172,
    185
   ],
   [
    55,
    57,
    63,
    138,
    148,
    180
   ],
   [
    45,
    56,
    58,
    139,
    149,
    181
   ],
   [
    46,
    57,
    59,
    140,
    150,
    182
   ],
   [
    47,
    58,
    60,
    108,
    141,
    151
   ],
   [
    48,
    59,
    61,
    109,
    142,
    152
   ],
   [
    0,
    49,
    60,
    110,
    143,
    153
   ],
   [
    50,
    61,
    62,
    111,
    144,
    154
   ],
   [
    45,
    52,
    62,
    113,
    146,
    155
   ],
   [
    46,
    53,
    63,
    147,
    156,
    176
   ],
   [
    64,
    66,
    71,
    128,
    148,
    157
   ],
   [
    55,
    65,
    67,
    149,
    158,
    183
   ],
   [
    56,
    66,
    68,
    150,
    159,
    184
   ],
   [
    57,
    67,
    69,
    114,
    151,
    160
   ],
   [
    58,
    68,
    70,
    115,
    152,
    161
   ],
   [
    1,
    59,
    69,
    116,
    153,
    162
   ],
   [
    2,
    60,
    70,
    117,
    154,
    163
   ],
   [
    56,
    62,
    71,
    120,
    156,
    164
   ],
   [
    64,
    72,
    74,
    137,
    158,
    165
   ],
   [
    65,
    73,
    75,
    159,
    166,
    185
   ],
   [
    66,
    74,
    76,
    121,
    160,
    167
   ],
   [
    67,
    75,
    77,
    122,
    161,
    168
   ],
   [
    3,
    68,
    76,
    123,
    162,
    169
   ],
   [
    4,
    69,
    77,
    124,
    163,
    170
   ],
   [
    72,
    78,
    80,
    147,
    166,
    171
   ],
   [
    73,
    79,
    81,
    129,
    167,
    172
   ],
   [
    74,
    80,
    82,
    130,
    168,
    173
   ],
   [
    6,
    75,
    81,
    131,
    169,
    174
   ],
   [
    7,
    76,
    82,
    132,
    170,
    175
   ],
   [
    78,
    83,
    85,
    138,
    172,
    176
   ],
   [
    79,
    84,
    86,
    139,
    173,
    177
   ],
   [
    10,
    80,
    85,
    140,
    174,
    178
   ],
   [
    11,
    81,
    86,
    141,
    175,
    179
   ],
   [
    83,
    87,
    89,
    149,
    177,
    180
   ],
   [
    15,
    84,
    88,
    150,
    178,
    181
   ],
   [
    16,
    85,
    89,
    151,
    179,
    182
   ],
   [
    21,
    87,
    90,
    159,
    181,
    183
   ],
   [
    22,
    88,
    91,
    160,
    182,
    184
   ],
   [
    29,
    90,
    92,
    167,
    184,
    185
   ]
  ]
 },
 "distance": {
  "d": 14,
  "X": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    6,
    23,
    49,
    60,
    70,
    96,
    104,
    108,
    109,
    116,
    123,
    131,
    152,
    162
   ]
  },
  "Z": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    0,
    6,
    12,
    18,
    33,
    41,
    50,
    61,
    70,
    96,
    104,
    110,
    117,
    143
   ]
  }
 },
 "provenance": {
  "authors": [
   "Zijian Liang",
   "Ke Liu",
   "Hao Song",
   "Yu-An Chen"
  ],
  "construction": "Twisted-torus bivariate-bicycle code from Generalized toric codes on twisted tori for quantum error correction (PRX Quantum 6, 020357, 2025). Stabilizers f(x,y)=1+x+x^2y^3, g(x,y)=1+y+x^2y^-2 on the abelian quotient group Z^2/L with twist basis a_1=[0, 31], a_2=[3, 7] (n=2|det[a_1,a_2]|=2*93). Reconstructed from the published polynomials and twist; CSS form H_X=[f|g], H_Z=[gbar|fbar].",
  "references": [
   "arXiv:2503.03827"
  ],
  "date": "2025",
  "notes": "Reconstructed baseline from Liang, Liu, Song, Chen, Generalized toric codes on twisted tori for quantum error correction (PRX Quantum 6, 020357, 2025), arXiv:2503.03827. The [[n,k,d]] parameter set and stabilizer polynomials are published in that paper; this entry reproduces them. Distance is an upper bound per the paper (probabilistic for d>20); the witness is the surrogate logical of that weight. Seeded to fill a board coverage gap at this block size, not a discovery.",
  "origin": "baseline",
  "novelty": "known_parameters"
 },
 "family": "bivariate-bicycle"
}