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