{
 "schema_version": "0.1",
 "name": "[[252,12,16]] twisted-torus BB code (arXiv:2503.03827)",
 "code_type": "CSS",
 "n": 252,
 "k": 12,
 "checks": {
  "X": [
   [
    0,
    1,
    61,
    126,
    128,
    229
   ],
   [
    1,
    3,
    72,
    127,
    130,
    237
   ],
   [
    2,
    4,
    73,
    128,
    131,
    238
   ],
   [
    3,
    6,
    83,
    129,
    133,
    243
   ],
   [
    4,
    7,
    84,
    130,
    134,
    244
   ],
   [
    5,
    8,
    85,
    129,
    131,
    135
   ],
   [
    6,
    10,
    94,
    132,
    137,
    247
   ],
   [
    7,
    11,
    95,
    133,
    138,
    248
   ],
   [
    8,
    12,
    96,
    132,
    134,
    139
   ],
   [
    9,
    13,
    97,
    133,
    135,
    140
   ],
   [
    10,
    15,
    104,
    136,
    142,
    249
   ],
   [
    0,
    11,
    16,
    137,
    143,
    250
   ],
   [
    12,
    17,
    105,
    136,
    138,
    144
   ],
   [
    13,
    18,
    106,
    137,
    139,
    145
   ],
   [
    14,
    19,
    107,
    138,
    140,
    146
   ],
   [
    15,
    21,
    112,
    141,
    148,
    180
   ],
   [
    1,
    16,
    22,
    142,
    149,
    251
   ],
   [
    2,
    17,
    23,
    141,
    143,
    150
   ],
   [
    18,
    24,
    113,
    142,
    144,
    151
   ],
   [
    19,
    25,
    114,
    143,
    145,
    152
   ],
   [
    20,
    26,
    66,
    144,
    146,
    153
   ],
   [
    21,
    28,
    118,
    147,
    155,
    190
   ],
   [
    3,
    22,
    29,
    148,
    156,
    191
   ],
   [
    4,
    23,
    30,
    147,
    149,
    157
   ],
   [
    5,
    24,
    31,
    148,
    150,
    158
   ],
   [
    25,
    32,
    119,
    149,
    151,
    159
   ],
   [
    26,
    33,
    77,
    150,
    152,
    160
   ],
   [
    27,
    34,
    78,
    151,
    153,
    161
   ],
   [
    28,
    36,
    122,
    154,
    163,
    201
   ],
   [
    6,
    29,
    37,
    155,
    164,
    202
   ],
   [
    7,
    30,
    38,
    154,
    156,
    165
   ],
   [
    8,
    31,
    39,
    155,
    157,
    166
   ],
   [
    9,
    32,
    40,
    156,
    158,
    167
   ],
   [
    33,
    41,
    88,
    157,
    159,
    168
   ],
   [
    34,
    42,
    89,
    158,
    160,
    169
   ],
   [
    35,
    43,
    90,
    159,
    161,
    170
   ],
   [
    36,
    45,
    124,
    162,
    172,
    212
   ],
   [
    10,
    37,
    46,
    163,
    173,
    213
   ],
   [
    11,
    38,
    47,
    162,
    164,
    174
   ],
   [
    12,
    39,
    48,
    163,
    165,
    175
   ],
   [
    13,
    40,
    49,
    164,
    166,
    176
   ],
   [
    14,
    41,
    50,
    165,
    167,
    177
   ],
   [
    42,
    51,
    99,
    166,
    168,
    178
   ],
   [
    43,
    52,
    100,
    167,
    169,
    179
   ],
   [
    44,
    53,
    101,
    168,
    170,
    180
   ],
   [
    45,
    55,
    125,
    171,
    182,
    223
   ],
   [
    15,
    46,
    56,
    172,
    183,
    224
   ],
   [
    16,
    47,
    57,
    171,
    173,
    184
   ],
   [
    17,
    48,
    58,
    172,
    174,
    185
   ],
   [
    18,
    49,
    59,
    173,
    175,
    186
   ],
   [
    19,
    50,
    60,
    174,
    176,
    187
   ],
   [
    20,
    51,
    61,
    175,
    177,
    188
   ],
   [
    52,
    62,
    108,
    176,
    178,
    189
   ],
   [
    53,
    63,
    109,
    177,
    179,
    190
   ],
   [
    54,
    64,
    110,
    178,
    180,
    191
   ],
   [
    55,
    65,
    66,
    181,
    193,
    232
   ],
   [
    21,
    56,
    67,
    182,
    194,
    233
   ],
   [
    22,
    57,
    68,
    181,
    183,
    195
   ],
   [
    23,
    58,
    69,
    182,
    184,
    196
   ],
   [
    24,
    59,
    70,
    183,
    185,
    197
   ],
   [
    25,
    60,
    71,
    184,
    186,
    198
   ],
   [
    26,
    61,
    72,
    185,
    187,
    199
   ],
   [
    27,
    62,
    73,
    186,
    188,
    200
   ],
   [
    63,
    74,
    115,
    187,
    189,
    201
   ],
   [
    64,
    75,
    116,
    188,
    190,
    202
   ],
   [
    65,
    76,
    117,
    154,
    189,
    191
   ],
   [
    66,
    76,
    77,
    192,
    204,
    239
   ],
   [
    28,
    67,
    78,
    193,
    205,
    240
   ],
   [
    29,
    68,
    79,
    192,
    194,
    206
   ],
   [
    30,
    69,
    80,
    193,
    195,
    207
   ],
   [
    31,
    70,
    81,
    194,
    196,
    208
   ],
   [
    32,
    71,
    82,
    195,
    197,
    209
   ],
   [
    33,
    72,
    83,
    196,
    198,
    210
   ],
   [
    34,
    73,
    84,
    197,
    199,
    211
   ],
   [
    35,
    74,
    85,
    198,
    200,
    212
   ],
   [
    75,
    86,
    120,
    199,
    201,
    213
   ],
   [
    76,
    87,
    121,
    162,
    200,
    202
   ],
   [
    77,
    87,
    88,
    131,
    203,
    215
   ],
   [
    36,
    78,
    89,
    204,
    216,
    245
   ],
   [
    37,
    79,
    90,
    203,
    205,
    217
   ],
   [
    38,
    80,
    91,
    204,
    206,
    218
   ],
   [
    39,
    81,
    92,
    205,
    207,
    219
   ],
   [
    40,
    82,
    93,
    206,
    208,
    220
   ],
   [
    41,
    83,
    94,
    207,
    209,
    221
   ],
   [
    42,
    84,
    95,
    208,
    210,
    222
   ],
   [
    43,
    85,
    96,
    209,
    211,
    223
   ],
   [
    44,
    86,
    97,
    210,
    212,
    224
   ],
   [
    87,
    98,
    123,
    171,
    211,
    213
   ],
   [
    14,
    88,
    98,
    134,
    214,
    225
   ],
   [
    45,
    89,
    99,
    135,
    215,
    226
   ],
   [
    46,
    90,
    100,
    214,
    216,
    227
   ],
   [
    47,
    91,
    101,
    215,
    217,
    228
   ],
   [
    48,
    92,
    102,
    216,
    218,
    229
   ],
   [
    49,
    93,
    103,
    217,
    219,
    230
   ],
   [
    50,
    94,
    104,
    126,
    218,
    220
   ],
   [
    0,
    51,
    95,
    219,
    221,
    231
   ],
   [
    52,
    96,
    105,
    220,
    222,
    232
   ],
   [
    53,
    97,
    106,
    221,
    223,
    233
   ],
   [
    54,
    98,
    107,
    181,
    222,
    224
   ],
   [
    20,
    55,
    99,
    139,
    225,
    234
   ],
   [
    56,
    100,
    108,
    140,
    226,
    235
   ],
   [
    57,
    101,
    109,
    225,
    227,
    236
   ],
   [
    58,
    102,
    110,
    226,
    228,
    237
   ],
   [
    59,
    103,
    111,
    227,
    229,
    238
   ],
   [
    60,
    104,
    112,
    127,
    228,
    230
   ],
   [
    2,
    62,
    105,
    230,
    231,
    239
   ],
   [
    63,
    106,
    113,
    126,
    232,
    240
   ],
   [
    64,
    107,
    114,
    192,
    231,
    233
   ],
   [
    27,
    67,
    108,
    145,
    234,
    241
   ],
   [
    68,
    109,
    115,
    146,
    235,
    242
   ],
   [
    69,
    110,
    116,
    234,
    236,
    243
   ],
   [
    70,
    111,
    117,
    235,
    237,
    244
   ],
   [
    71,
    112,
    118,
    129,
    236,
    238
   ],
   [
    5,
    74,
    113,
    127,
    239,
    245
   ],
   [
    75,
    114,
    119,
    128,
    203,
    240
   ],
   [
    35,
    79,
    115,
    152,
    241,
    246
   ],
   [
    80,
    116,
    120,
    153,
    242,
    247
   ],
   [
    81,
    117,
    121,
    241,
    243,
    248
   ],
   [
    82,
    118,
    122,
    132,
    242,
    244
   ],
   [
    9,
    86,
    119,
    130,
    214,
    245
   ],
   [
    44,
    91,
    120,
    160,
    246,
    249
   ],
   [
    92,
    121,
    123,
    161,
    247,
    250
   ],
   [
    93,
    122,
    124,
    136,
    246,
    248
   ],
   [
    54,
    102,
    123,
    169,
    249,
    251
   ],
   [
    103,
    124,
    125,
    141,
    170,
    250
   ],
   [
    65,
    111,
    125,
    147,
    179,
    251
   ]
  ],
  "Z": [
   [
    0,
    94,
    106,
    126,
    137,
    221
   ],
   [
    1,
    104,
    113,
    126,
    127,
    142
   ],
   [
    0,
    2,
    114,
    128,
    143,
    231
   ],
   [
    3,
    5,
    112,
    127,
    129,
    148
   ],
   [
    1,
    4,
    119,
    128,
    130,
    149
   ],
   [
    2,
    5,
    77,
    131,
    150,
    239
   ],
   [
    6,
    8,
    118,
    129,
    132,
    155
   ],
   [
    3,
    7,
    9,
    130,
    133,
    156
   ],
   [
    4,
    8,
    88,
    131,
    134,
    157
   ],
   [
    5,
    9,
    89,
    135,
    158,
    245
   ],
   [
    10,
    12,
    122,
    132,
    136,
    163
   ],
   [
    6,
    11,
    13,
    133,
    137,
    164
   ],
   [
    7,
    12,
    14,
    134,
    138,
    165
   ],
   [
    8,
    13,
    99,
    135,
    139,
    166
   ],
   [
    9,
    14,
    100,
    140,
    167,
    214
   ],
   [
    15,
    17,
    124,
    136,
    141,
    172
   ],
   [
    10,
    16,
    18,
    137,
    142,
    173
   ],
   [
    11,
    17,
    19,
    138,
    143,
    174
   ],
   [
    12,
    18,
    20,
    139,
    144,
    175
   ],
   [
    13,
    19,
    108,
    140,
    145,
    176
   ],
   [
    14,
    20,
    109,
    146,
    177,
    225
   ],
   [
    21,
    23,
    125,
    141,
    147,
    182
   ],
   [
    15,
    22,
    24,
    142,
    148,
    183
   ],
   [
    16,
    23,
    25,
    143,
    149,
    184
   ],
   [
    17,
    24,
    26,
    144,
    150,
    185
   ],
   [
    18,
    25,
    27,
    145,
    151,
    186
   ],
   [
    19,
    26,
    115,
    146,
    152,
    187
   ],
   [
    20,
    27,
    116,
    153,
    188,
    234
   ],
   [
    28,
    30,
    65,
    147,
    154,
    193
   ],
   [
    21,
    29,
    31,
    148,
    155,
    194
   ],
   [
    22,
    30,
    32,
    149,
    156,
    195
   ],
   [
    23,
    31,
    33,
    150,
    157,
    196
   ],
   [
    24,
    32,
    34,
    151,
    158,
    197
   ],
   [
    25,
    33,
    35,
    152,
    159,
    198
   ],
   [
    26,
    34,
    120,
    153,
    160,
    199
   ],
   [
    27,
    35,
    121,
    161,
    200,
    241
   ],
   [
    36,
    38,
    76,
    154,
    162,
    204
   ],
   [
    28,
    37,
    39,
    155,
    163,
    205
   ],
   [
    29,
    38,
    40,
    156,
    164,
    206
   ],
   [
    30,
    39,
    41,
    157,
    165,
    207
   ],
   [
    31,
    40,
    42,
    158,
    166,
    208
   ],
   [
    32,
    41,
    43,
    159,
    167,
    209
   ],
   [
    33,
    42,
    44,
    160,
    168,
    210
   ],
   [
    34,
    43,
    123,
    161,
    169,
    211
   ],
   [
    35,
    44,
    124,
    170,
    212,
    246
   ],
   [
    45,
    47,
    87,
    162,
    171,
    215
   ],
   [
    36,
    46,
    48,
    163,
    172,
    216
   ],
   [
    37,
    47,
    49,
    164,
    173,
    217
   ],
   [
    38,
    48,
    50,
    165,
    174,
    218
   ],
   [
    39,
    49,
    51,
    166,
    175,
    219
   ],
   [
    40,
    50,
    52,
    167,
    176,
    220
   ],
   [
    41,
    51,
    53,
    168,
    177,
    221
   ],
   [
    42,
    52,
    54,
    169,
    178,
    222
   ],
   [
    43,
    53,
    125,
    170,
    179,
    223
   ],
   [
    15,
    44,
    54,
    180,
    224,
    249
   ],
   [
    55,
    57,
    98,
    171,
    181,
    225
   ],
   [
    45,
    56,
    58,
    172,
    182,
    226
   ],
   [
    46,
    57,
    59,
    173,
    183,
    227
   ],
   [
    47,
    58,
    60,
    174,
    184,
    228
   ],
   [
    48,
    59,
    61,
    175,
    185,
    229
   ],
   [
    49,
    60,
    62,
    176,
    186,
    230
   ],
   [
    50,
    61,
    63,
    126,
    177,
    187
   ],
   [
    51,
    62,
    64,
    178,
    188,
    231
   ],
   [
    52,
    63,
    65,
    179,
    189,
    232
   ],
   [
    21,
    53,
    64,
    180,
    190,
    233
   ],
   [
    22,
    54,
    65,
    181,
    191,
    251
   ],
   [
    66,
    68,
    107,
    146,
    181,
    192
   ],
   [
    55,
    67,
    69,
    182,
    193,
    234
   ],
   [
    56,
    68,
    70,
    183,
    194,
    235
   ],
   [
    57,
    69,
    71,
    184,
    195,
    236
   ],
   [
    58,
    70,
    72,
    185,
    196,
    237
   ],
   [
    59,
    71,
    73,
    186,
    197,
    238
   ],
   [
    60,
    72,
    74,
    127,
    187,
    198
   ],
   [
    61,
    73,
    75,
    128,
    188,
    199
   ],
   [
    62,
    74,
    76,
    189,
    200,
    239
   ],
   [
    28,
    63,
    75,
    190,
    201,
    240
   ],
   [
    29,
    64,
    76,
    191,
    192,
    202
   ],
   [
    77,
    79,
    114,
    152,
    192,
    203
   ],
   [
    66,
    78,
    80,
    153,
    193,
    204
   ],
   [
    67,
    79,
    81,
    194,
    205,
    241
   ],
   [
    68,
    80,
    82,
    195,
    206,
    242
   ],
   [
    69,
    81,
    83,
    196,
    207,
    243
   ],
   [
    70,
    82,
    84,
    197,
    208,
    244
   ],
   [
    71,
    83,
    85,
    129,
    198,
    209
   ],
   [
    72,
    84,
    86,
    130,
    199,
    210
   ],
   [
    73,
    85,
    87,
    131,
    200,
    211
   ],
   [
    36,
    74,
    86,
    201,
    212,
    245
   ],
   [
    37,
    75,
    87,
    202,
    203,
    213
   ],
   [
    88,
    90,
    119,
    159,
    203,
    214
   ],
   [
    77,
    89,
    91,
    160,
    204,
    215
   ],
   [
    78,
    90,
    92,
    161,
    205,
    216
   ],
   [
    79,
    91,
    93,
    206,
    217,
    246
   ],
   [
    80,
    92,
    94,
    207,
    218,
    247
   ],
   [
    81,
    93,
    95,
    208,
    219,
    248
   ],
   [
    82,
    94,
    96,
    132,
    209,
    220
   ],
   [
    83,
    95,
    97,
    133,
    210,
    221
   ],
   [
    84,
    96,
    98,
    134,
    211,
    222
   ],
   [
    45,
    85,
    97,
    135,
    212,
    223
   ],
   [
    46,
    86,
    98,
    213,
    214,
    224
   ],
   [
    88,
    99,
    101,
    168,
    215,
    225
   ],
   [
    89,
    100,
    102,
    169,
    216,
    226
   ],
   [
    90,
    101,
    103,
    170,
    217,
    227
   ],
   [
    91,
    102,
    104,
    218,
    228,
    249
   ],
   [
    0,
    92,
    103,
    219,
    229,
    250
   ],
   [
    93,
    104,
    105,
    136,
    220,
    230
   ],
   [
    95,
    105,
    107,
    138,
    222,
    231
   ],
   [
    55,
    96,
    106,
    139,
    223,
    232
   ],
   [
    56,
    97,
    107,
    140,
    224,
    233
   ],
   [
    99,
    108,
    110,
    178,
    226,
    234
   ],
   [
    100,
    109,
    111,
    179,
    227,
    235
   ],
   [
    101,
    110,
    112,
    180,
    228,
    236
   ],
   [
    1,
    102,
    111,
    229,
    237,
    251
   ],
   [
    2,
    103,
    112,
    141,
    230,
    238
   ],
   [
    66,
    105,
    113,
    144,
    232,
    239
   ],
   [
    67,
    106,
    114,
    145,
    233,
    240
   ],
   [
    108,
    115,
    117,
    189,
    235,
    241
   ],
   [
    109,
    116,
    118,
    190,
    236,
    242
   ],
   [
    3,
    110,
    117,
    191,
    237,
    243
   ],
   [
    4,
    111,
    118,
    147,
    238,
    244
   ],
   [
    78,
    113,
    119,
    151,
    240,
    245
   ],
   [
    115,
    120,
    122,
    201,
    242,
    246
   ],
   [
    6,
    116,
    121,
    202,
    243,
    247
   ],
   [
    7,
    117,
    122,
    154,
    244,
    248
   ],
   [
    10,
    120,
    123,
    213,
    247,
    249
   ],
   [
    11,
    121,
    124,
    162,
    248,
    250
   ],
   [
    16,
    123,
    125,
    171,
    250,
    251
   ]
  ]
 },
 "distance": {
  "d": 16,
  "X": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": [
    6,
    11,
    17,
    29,
    31,
    40,
    132,
    136,
    185,
    191,
    196,
    220,
    229,
    243,
    250,
    251
   ]
  },
  "Z": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": [
    4,
    6,
    17,
    23,
    62,
    73,
    83,
    84,
    94,
    105,
    164,
    174,
    176,
    196,
    208,
    220
   ]
  }
 },
 "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^-3y^-1, g(x,y)=1+y+x^2y^-2 on the abelian quotient group Z^2/L with twist basis a_1=[0, 18], a_2=[7, 7] (n=2|det[a_1,a_2]|=2*126). 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"
}