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   ],
   [
    81,
    91,
    116,
    213,
    219,
    269
   ],
   [
    75,
    82,
    92,
    214,
    220,
    231
   ],
   [
    51,
    76,
    83,
    215,
    221,
    232
   ],
   [
    52,
    77,
    84,
    216,
    222,
    233
   ],
   [
    53,
    78,
    85,
    217,
    223,
    234
   ],
   [
    54,
    79,
    86,
    218,
    224,
    235
   ],
   [
    87,
    97,
    122,
    219,
    225,
    272
   ],
   [
    81,
    88,
    98,
    220,
    226,
    237
   ],
   [
    57,
    82,
    89,
    221,
    227,
    238
   ],
   [
    58,
    83,
    90,
    222,
    228,
    239
   ],
   [
    59,
    84,
    91,
    223,
    229,
    240
   ],
   [
    60,
    85,
    92,
    224,
    230,
    241
   ],
   [
    93,
    103,
    127,
    225,
    231,
    274
   ],
   [
    87,
    94,
    104,
    226,
    232,
    243
   ],
   [
    63,
    88,
    95,
    227,
    233,
    244
   ],
   [
    64,
    89,
    96,
    228,
    234,
    245
   ],
   [
    65,
    90,
    97,
    229,
    235,
    246
   ],
   [
    66,
    91,
    98,
    230,
    236,
    247
   ],
   [
    99,
    109,
    131,
    231,
    237,
    275
   ],
   [
    93,
    100,
    110,
    232,
    238,
    249
   ],
   [
    69,
    94,
    101,
    233,
    239,
    250
   ],
   [
    70,
    95,
    102,
    234,
    240,
    251
   ],
   [
    71,
    96,
    103,
    235,
    241,
    252
   ],
   [
    72,
    97,
    104,
    236,
    242,
    253
   ],
   [
    105,
    115,
    134,
    138,
    237,
    243
   ],
   [
    99,
    106,
    116,
    238,
    244,
    255
   ],
   [
    75,
    100,
    107,
    239,
    245,
    256
   ],
   [
    76,
    101,
    108,
    240,
    246,
    257
   ],
   [
    77,
    102,
    109,
    241,
    247,
    258
   ],
   [
    78,
    103,
    110,
    242,
    248,
    259
   ],
   [
    111,
    121,
    136,
    139,
    243,
    249
   ],
   [
    105,
    112,
    122,
    140,
    244,
    250
   ],
   [
    81,
    106,
    113,
    245,
    251,
    261
   ],
   [
    82,
    107,
    114,
    246,
    252,
    262
   ],
   [
    83,
    108,
    115,
    247,
    253,
    263
   ],
   [
    84,
    109,
    116,
    248,
    254,
    264
   ],
   [
    117,
    126,
    137,
    141,
    249,
    255
   ],
   [
    111,
    118,
    127,
    142,
    250,
    256
   ],
   [
    87,
    112,
    119,
    143,
    251,
    257
   ],
   [
    88,
    113,
    120,
    252,
    258,
    266
   ],
   [
    89,
    114,
    121,
    253,
    259,
    267
   ],
   [
    90,
    115,
    122,
    254,
    260,
    268
   ],
   [
    117,
    123,
    131,
    145,
    256,
    261
   ],
   [
    93,
    118,
    124,
    146,
    257,
    262
   ],
   [
    94,
    119,
    125,
    147,
    258,
    263
   ],
   [
    95,
    120,
    126,
    259,
    264,
    270
   ],
   [
    96,
    121,
    127,
    260,
    265,
    271
   ],
   [
    99,
    123,
    128,
    150,
    262,
    266
   ],
   [
    100,
    124,
    129,
    151,
    263,
    267
   ],
   [
    101,
    125,
    130,
    152,
    264,
    268
   ],
   [
    102,
    126,
    131,
    265,
    269,
    273
   ],
   [
    106,
    128,
    132,
    156,
    267,
    270
   ],
   [
    107,
    129,
    133,
    157,
    268,
    271
   ],
   [
    108,
    130,
    134,
    158,
    269,
    272
   ],
   [
    113,
    132,
    135,
    163,
    271,
    273
   ],
   [
    114,
    133,
    136,
    164,
    272,
    274
   ],
   [
    120,
    135,
    137,
    170,
    274,
    275
   ]
  ]
 },
 "distance": {
  "d": 24,
  "X": {
   "value": 24,
   "confidence": "upper_bound",
   "witness": [
    3,
    4,
    12,
    29,
    36,
    113,
    120,
    135,
    146,
    148,
    156,
    162,
    188,
    199,
    200,
    205,
    206,
    211,
    217,
    223,
    240,
    251,
    257,
    270
   ]
  },
  "Z": {
   "value": 24,
   "confidence": "upper_bound",
   "witness": [
    13,
    18,
    23,
    24,
    35,
    72,
    77,
    83,
    84,
    112,
    122,
    130,
    152,
    162,
    204,
    216,
    219,
    225,
    229,
    232,
    242,
    251,
    258,
    264
   ]
  }
 },
 "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, g(x,y)=1+y+x^3y^2 on the abelian quotient group Z^2/L with twist basis a_1=[0, 6], a_2=[23, 5] (n=2|det[a_1,a_2]|=2*138). 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"
}