{
 "schema_version": "0.1",
 "name": "[[162,8,14]] twisted-torus BB code (arXiv:2503.03827)",
 "code_type": "CSS",
 "n": 162,
 "k": 8,
 "checks": {
  "X": [
   [
    0,
    1,
    36,
    81,
    83,
    146
   ],
   [
    1,
    3,
    9,
    82,
    85,
    151
   ],
   [
    2,
    4,
    45,
    83,
    86,
    87
   ],
   [
    3,
    6,
    13,
    84,
    88,
    155
   ],
   [
    4,
    7,
    14,
    85,
    89,
    91
   ],
   [
    5,
    8,
    53,
    86,
    90,
    92
   ],
   [
    6,
    10,
    18,
    87,
    92,
    158
   ],
   [
    7,
    11,
    19,
    88,
    93,
    96
   ],
   [
    8,
    12,
    20,
    89,
    94,
    97
   ],
   [
    9,
    13,
    60,
    90,
    95,
    98
   ],
   [
    10,
    15,
    24,
    91,
    97,
    160
   ],
   [
    11,
    16,
    25,
    92,
    98,
    102
   ],
   [
    12,
    17,
    26,
    93,
    99,
    103
   ],
   [
    13,
    18,
    27,
    94,
    100,
    104
   ],
   [
    14,
    19,
    66,
    95,
    101,
    105
   ],
   [
    15,
    21,
    31,
    96,
    103,
    161
   ],
   [
    16,
    22,
    32,
    97,
    104,
    109
   ],
   [
    17,
    23,
    33,
    98,
    105,
    110
   ],
   [
    18,
    24,
    34,
    99,
    106,
    111
   ],
   [
    19,
    25,
    35,
    100,
    107,
    112
   ],
   [
    20,
    26,
    71,
    101,
    108,
    113
   ],
   [
    21,
    28,
    39,
    86,
    102,
    110
   ],
   [
    22,
    29,
    40,
    103,
    111,
    117
   ],
   [
    23,
    30,
    41,
    104,
    112,
    118
   ],
   [
    24,
    31,
    42,
    105,
    113,
    119
   ],
   [
    25,
    32,
    43,
    106,
    114,
    120
   ],
   [
    26,
    33,
    44,
    107,
    115,
    121
   ],
   [
    27,
    34,
    75,
    108,
    116,
    122
   ],
   [
    28,
    36,
    47,
    89,
    109,
    118
   ],
   [
    29,
    37,
    48,
    90,
    110,
    119
   ],
   [
    30,
    38,
    49,
    111,
    120,
    126
   ],
   [
    31,
    39,
    50,
    112,
    121,
    127
   ],
   [
    32,
    40,
    51,
    113,
    122,
    128
   ],
   [
    33,
    41,
    52,
    114,
    123,
    129
   ],
   [
    0,
    34,
    42,
    115,
    124,
    130
   ],
   [
    35,
    43,
    78,
    116,
    125,
    131
   ],
   [
    9,
    36,
    54,
    93,
    117,
    126
   ],
   [
    37,
    45,
    55,
    94,
    118,
    127
   ],
   [
    38,
    46,
    56,
    95,
    119,
    128
   ],
   [
    39,
    47,
    57,
    120,
    129,
    134
   ],
   [
    40,
    48,
    58,
    121,
    130,
    135
   ],
   [
    41,
    49,
    59,
    122,
    131,
    136
   ],
   [
    1,
    42,
    50,
    123,
    132,
    137
   ],
   [
    2,
    43,
    51,
    124,
    133,
    138
   ],
   [
    44,
    52,
    80,
    81,
    125,
    139
   ],
   [
    14,
    45,
    61,
    99,
    126,
    134
   ],
   [
    46,
    53,
    62,
    100,
    127,
    135
   ],
   [
    47,
    54,
    63,
    101,
    128,
    136
   ],
   [
    48,
    55,
    64,
    129,
    137,
    141
   ],
   [
    49,
    56,
    65,
    130,
    138,
    142
   ],
   [
    3,
    50,
    57,
    131,
    139,
    143
   ],
   [
    4,
    51,
    58,
    132,
    140,
    144
   ],
   [
    5,
    52,
    59,
    82,
    133,
    145
   ],
   [
    20,
    53,
    67,
    106,
    134,
    141
   ],
   [
    54,
    60,
    68,
    107,
    135,
    142
   ],
   [
    55,
    61,
    69,
    108,
    136,
    143
   ],
   [
    56,
    62,
    70,
    137,
    144,
    147
   ],
   [
    6,
    57,
    63,
    138,
    145,
    148
   ],
   [
    7,
    58,
    64,
    139,
    146,
    149
   ],
   [
    8,
    59,
    65,
    84,
    140,
    150
   ],
   [
    27,
    60,
    72,
    114,
    141,
    147
   ],
   [
    61,
    66,
    73,
    115,
    142,
    148
   ],
   [
    62,
    67,
    74,
    116,
    143,
    149
   ],
   [
    10,
    63,
    68,
    144,
    150,
    152
   ],
   [
    11,
    64,
    69,
    145,
    151,
    153
   ],
   [
    12,
    65,
    70,
    87,
    146,
    154
   ],
   [
    35,
    66,
    76,
    123,
    147,
    152
   ],
   [
    67,
    71,
    77,
    124,
    148,
    153
   ],
   [
    15,
    68,
    72,
    125,
    149,
    154
   ],
   [
    16,
    69,
    73,
    150,
    155,
    156
   ],
   [
    17,
    70,
    74,
    91,
    151,
    157
   ],
   [
    44,
    71,
    79,
    132,
    152,
    156
   ],
   [
    21,
    72,
    75,
    133,
    153,
    157
   ],
   [
    22,
    73,
    76,
    81,
    154,
    158
   ],
   [
    23,
    74,
    77,
    96,
    155,
    159
   ],
   [
    0,
    28,
    75,
    140,
    156,
    159
   ],
   [
    29,
    76,
    78,
    82,
    157,
    160
   ],
   [
    30,
    77,
    79,
    83,
    102,
    158
   ],
   [
    2,
    37,
    78,
    84,
    159,
    161
   ],
   [
    38,
    79,
    80,
    85,
    109,
    160
   ],
   [
    5,
    46,
    80,
    88,
    117,
    161
   ]
  ],
  "Z": [
   [
    0,
    44,
    73,
    81,
    115,
    156
   ],
   [
    1,
    52,
    76,
    81,
    82,
    123
   ],
   [
    0,
    2,
    77,
    83,
    124,
    159
   ],
   [
    3,
    59,
    78,
    82,
    84,
    131
   ],
   [
    1,
    4,
    79,
    83,
    85,
    132
   ],
   [
    2,
    5,
    21,
    86,
    133,
    161
   ],
   [
    2,
    6,
    65,
    84,
    87,
    138
   ],
   [
    3,
    7,
    80,
    85,
    88,
    139
   ],
   [
    4,
    8,
    28,
    86,
    89,
    140
   ],
   [
    5,
    9,
    29,
    82,
    90,
    117
   ],
   [
    4,
    10,
    70,
    87,
    91,
    144
   ],
   [
    5,
    6,
    11,
    88,
    92,
    145
   ],
   [
    7,
    12,
    36,
    89,
    93,
    146
   ],
   [
    8,
    13,
    37,
    84,
    90,
    94
   ],
   [
    9,
    14,
    38,
    85,
    95,
    126
   ],
   [
    7,
    15,
    74,
    91,
    96,
    149
   ],
   [
    8,
    10,
    16,
    92,
    97,
    150
   ],
   [
    9,
    11,
    17,
    93,
    98,
    151
   ],
   [
    12,
    18,
    45,
    87,
    94,
    99
   ],
   [
    13,
    19,
    46,
    88,
    95,
    100
   ],
   [
    14,
    20,
    47,
    89,
    101,
    134
   ],
   [
    11,
    21,
    77,
    96,
    102,
    153
   ],
   [
    12,
    15,
    22,
    97,
    103,
    154
   ],
   [
    13,
    16,
    23,
    98,
    104,
    155
   ],
   [
    14,
    17,
    24,
    91,
    99,
    105
   ],
   [
    18,
    25,
    53,
    92,
    100,
    106
   ],
   [
    19,
    26,
    54,
    93,
    101,
    107
   ],
   [
    20,
    27,
    55,
    94,
    108,
    141
   ],
   [
    16,
    28,
    79,
    102,
    109,
    156
   ],
   [
    17,
    21,
    29,
    103,
    110,
    157
   ],
   [
    18,
    22,
    30,
    104,
    111,
    158
   ],
   [
    19,
    23,
    31,
    96,
    105,
    112
   ],
   [
    20,
    24,
    32,
    97,
    106,
    113
   ],
   [
    25,
    33,
    60,
    98,
    107,
    114
   ],
   [
    26,
    34,
    61,
    99,
    108,
    115
   ],
   [
    27,
    35,
    62,
    100,
    116,
    147
   ],
   [
    22,
    36,
    80,
    81,
    109,
    117
   ],
   [
    23,
    28,
    37,
    110,
    118,
    159
   ],
   [
    24,
    29,
    38,
    111,
    119,
    160
   ],
   [
    25,
    30,
    39,
    102,
    112,
    120
   ],
   [
    26,
    31,
    40,
    103,
    113,
    121
   ],
   [
    27,
    32,
    41,
    104,
    114,
    122
   ],
   [
    33,
    42,
    66,
    105,
    115,
    123
   ],
   [
    34,
    43,
    67,
    106,
    116,
    124
   ],
   [
    35,
    44,
    68,
    107,
    125,
    152
   ],
   [
    30,
    36,
    45,
    83,
    118,
    126
   ],
   [
    31,
    37,
    46,
    119,
    127,
    161
   ],
   [
    32,
    38,
    47,
    109,
    120,
    128
   ],
   [
    33,
    39,
    48,
    110,
    121,
    129
   ],
   [
    34,
    40,
    49,
    111,
    122,
    130
   ],
   [
    35,
    41,
    50,
    112,
    123,
    131
   ],
   [
    42,
    51,
    71,
    113,
    124,
    132
   ],
   [
    43,
    52,
    72,
    114,
    125,
    133
   ],
   [
    39,
    45,
    53,
    86,
    127,
    134
   ],
   [
    40,
    46,
    54,
    117,
    128,
    135
   ],
   [
    41,
    47,
    55,
    118,
    129,
    136
   ],
   [
    42,
    48,
    56,
    119,
    130,
    137
   ],
   [
    43,
    49,
    57,
    120,
    131,
    138
   ],
   [
    44,
    50,
    58,
    121,
    132,
    139
   ],
   [
    51,
    59,
    75,
    122,
    133,
    140
   ],
   [
    48,
    53,
    60,
    90,
    135,
    141
   ],
   [
    49,
    54,
    61,
    126,
    136,
    142
   ],
   [
    50,
    55,
    62,
    127,
    137,
    143
   ],
   [
    51,
    56,
    63,
    128,
    138,
    144
   ],
   [
    52,
    57,
    64,
    129,
    139,
    145
   ],
   [
    0,
    58,
    65,
    130,
    140,
    146
   ],
   [
    56,
    60,
    66,
    95,
    142,
    147
   ],
   [
    57,
    61,
    67,
    134,
    143,
    148
   ],
   [
    58,
    62,
    68,
    135,
    144,
    149
   ],
   [
    59,
    63,
    69,
    136,
    145,
    150
   ],
   [
    1,
    64,
    70,
    137,
    146,
    151
   ],
   [
    63,
    66,
    71,
    101,
    148,
    152
   ],
   [
    64,
    67,
    72,
    141,
    149,
    153
   ],
   [
    65,
    68,
    73,
    142,
    150,
    154
   ],
   [
    3,
    69,
    74,
    143,
    151,
    155
   ],
   [
    69,
    71,
    75,
    108,
    153,
    156
   ],
   [
    70,
    72,
    76,
    147,
    154,
    157
   ],
   [
    6,
    73,
    77,
    148,
    155,
    158
   ],
   [
    74,
    75,
    78,
    116,
    157,
    159
   ],
   [
    10,
    76,
    79,
    152,
    158,
    160
   ],
   [
    15,
    78,
    80,
    125,
    160,
    161
   ]
  ]
 },
 "distance": {
  "d": 14,
  "X": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    9,
    14,
    24,
    29,
    69,
    75,
    89,
    97,
    140,
    146,
    150,
    151,
    154,
    157
   ]
  },
  "Z": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    2,
    4,
    7,
    44,
    58,
    77,
    79,
    80,
    96,
    115,
    130,
    138,
    148,
    161
   ]
  }
 },
 "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^-1y^3, g(x,y)=1+y+x^3y^-1 on the abelian quotient group Z^2/L with twist basis a_1=[0, 9], a_2=[9, -3] (n=2|det[a_1,a_2]|=2*81). 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"
}
