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