{
 "schema_version": "0.1",
 "name": "[[78,4,10]] twisted-torus BB code (arXiv:2503.03827)",
 "code_type": "CSS",
 "n": 78,
 "k": 4,
 "checks": {
  "X": [
   [
    0,
    1,
    30,
    39,
    41,
    46
   ],
   [
    1,
    3,
    33,
    40,
    43,
    49
   ],
   [
    2,
    4,
    34,
    41,
    44,
    50
   ],
   [
    3,
    5,
    6,
    42,
    46,
    52
   ],
   [
    4,
    7,
    36,
    43,
    47,
    53
   ],
   [
    5,
    8,
    37,
    39,
    42,
    44
   ],
   [
    6,
    8,
    9,
    45,
    49,
    55
   ],
   [
    0,
    7,
    10,
    46,
    50,
    56
   ],
   [
    8,
    11,
    38,
    40,
    45,
    47
   ],
   [
    9,
    11,
    12,
    48,
    52,
    58
   ],
   [
    1,
    10,
    13,
    49,
    53,
    59
   ],
   [
    2,
    11,
    14,
    42,
    48,
    50
   ],
   [
    12,
    14,
    15,
    51,
    55,
    61
   ],
   [
    3,
    13,
    16,
    52,
    56,
    62
   ],
   [
    4,
    14,
    17,
    45,
    51,
    53
   ],
   [
    15,
    17,
    18,
    54,
    58,
    64
   ],
   [
    6,
    16,
    19,
    55,
    59,
    65
   ],
   [
    7,
    17,
    20,
    48,
    54,
    56
   ],
   [
    18,
    20,
    21,
    57,
    61,
    67
   ],
   [
    9,
    19,
    22,
    58,
    62,
    68
   ],
   [
    10,
    20,
    23,
    51,
    57,
    59
   ],
   [
    21,
    23,
    24,
    60,
    64,
    70
   ],
   [
    12,
    22,
    25,
    61,
    65,
    71
   ],
   [
    13,
    23,
    26,
    54,
    60,
    62
   ],
   [
    24,
    26,
    27,
    63,
    67,
    73
   ],
   [
    15,
    25,
    28,
    64,
    68,
    74
   ],
   [
    16,
    26,
    29,
    57,
    63,
    65
   ],
   [
    27,
    29,
    30,
    66,
    70,
    75
   ],
   [
    18,
    28,
    31,
    67,
    71,
    76
   ],
   [
    19,
    29,
    32,
    60,
    66,
    68
   ],
   [
    30,
    32,
    33,
    39,
    69,
    73
   ],
   [
    21,
    31,
    34,
    70,
    74,
    77
   ],
   [
    22,
    32,
    35,
    63,
    69,
    71
   ],
   [
    5,
    33,
    35,
    40,
    72,
    75
   ],
   [
    24,
    34,
    36,
    41,
    73,
    76
   ],
   [
    25,
    35,
    37,
    66,
    72,
    74
   ],
   [
    0,
    27,
    36,
    43,
    75,
    77
   ],
   [
    28,
    37,
    38,
    44,
    69,
    76
   ],
   [
    2,
    31,
    38,
    47,
    72,
    77
   ]
  ],
  "Z": [
   [
    0,
    5,
    30,
    39,
    46,
    75
   ],
   [
    1,
    8,
    33,
    39,
    40,
    49
   ],
   [
    0,
    2,
    34,
    41,
    50,
    77
   ],
   [
    3,
    5,
    11,
    40,
    42,
    52
   ],
   [
    1,
    4,
    36,
    41,
    43,
    53
   ],
   [
    2,
    5,
    37,
    42,
    44,
    72
   ],
   [
    6,
    8,
    14,
    42,
    45,
    55
   ],
   [
    0,
    3,
    7,
    43,
    46,
    56
   ],
   [
    4,
    8,
    38,
    44,
    45,
    47
   ],
   [
    9,
    11,
    17,
    45,
    48,
    58
   ],
   [
    1,
    6,
    10,
    46,
    49,
    59
   ],
   [
    2,
    7,
    11,
    47,
    48,
    50
   ],
   [
    12,
    14,
    20,
    48,
    51,
    61
   ],
   [
    3,
    9,
    13,
    49,
    52,
    62
   ],
   [
    4,
    10,
    14,
    50,
    51,
    53
   ],
   [
    15,
    17,
    23,
    51,
    54,
    64
   ],
   [
    6,
    12,
    16,
    52,
    55,
    65
   ],
   [
    7,
    13,
    17,
    53,
    54,
    56
   ],
   [
    18,
    20,
    26,
    54,
    57,
    67
   ],
   [
    9,
    15,
    19,
    55,
    58,
    68
   ],
   [
    10,
    16,
    20,
    56,
    57,
    59
   ],
   [
    21,
    23,
    29,
    57,
    60,
    70
   ],
   [
    12,
    18,
    22,
    58,
    61,
    71
   ],
   [
    13,
    19,
    23,
    59,
    60,
    62
   ],
   [
    24,
    26,
    32,
    60,
    63,
    73
   ],
   [
    15,
    21,
    25,
    61,
    64,
    74
   ],
   [
    16,
    22,
    26,
    62,
    63,
    65
   ],
   [
    27,
    29,
    35,
    63,
    66,
    75
   ],
   [
    18,
    24,
    28,
    64,
    67,
    76
   ],
   [
    19,
    25,
    29,
    65,
    66,
    68
   ],
   [
    30,
    32,
    37,
    39,
    66,
    69
   ],
   [
    21,
    27,
    31,
    67,
    70,
    77
   ],
   [
    22,
    28,
    32,
    68,
    69,
    71
   ],
   [
    33,
    35,
    38,
    40,
    69,
    72
   ],
   [
    24,
    30,
    34,
    41,
    70,
    73
   ],
   [
    25,
    31,
    35,
    71,
    72,
    74
   ],
   [
    27,
    33,
    36,
    43,
    73,
    75
   ],
   [
    28,
    34,
    37,
    44,
    74,
    76
   ],
   [
    31,
    36,
    38,
    47,
    76,
    77
   ]
  ]
 },
 "distance": {
  "d": 10,
  "X": {
   "value": 10,
   "confidence": "upper_bound",
   "witness": [
    18,
    21,
    25,
    27,
    32,
    66,
    67,
    70,
    71,
    73
   ]
  },
  "Z": {
   "value": 10,
   "confidence": "upper_bound",
   "witness": [
    1,
    8,
    32,
    35,
    39,
    43,
    45,
    53,
    66,
    75
   ]
  }
 },
 "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^-2y^-1, g(x,y)=1+y+x^2y on the abelian quotient group Z^2/L with twist basis a_1=[0, 3], a_2=[13, 1] (n=2|det[a_1,a_2]|=2*39). 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"
}