{
 "schema_version": "0.1",
 "name": "[[162,54,3]] 2BGA",
 "code_type": "CSS",
 "n": 162,
 "k": 54,
 "checks": {
  "X": [
   [
    0,
    12,
    81,
    90,
    93,
    117,
    125,
    152
   ],
   [
    1,
    21,
    81,
    82,
    93,
    99,
    102,
    138
   ],
   [
    2,
    26,
    81,
    83,
    93,
    107,
    151,
    159
   ],
   [
    0,
    3,
    81,
    84,
    90,
    105,
    117,
    137
   ],
   [
    4,
    29,
    85,
    86,
    106,
    110,
    115,
    144
   ],
   [
    5,
    34,
    82,
    86,
    102,
    112,
    115,
    147
   ],
   [
    6,
    39,
    82,
    87,
    91,
    102,
    107,
    120
   ],
   [
    1,
    7,
    81,
    82,
    84,
    88,
    99,
    118
   ],
   [
    8,
    42,
    85,
    89,
    110,
    119,
    123,
    153
   ],
   [
    9,
    44,
    83,
    90,
    107,
    125,
    149,
    158
   ],
   [
    2,
    10,
    81,
    83,
    84,
    91,
    135,
    159
   ],
   [
    11,
    47,
    85,
    92,
    110,
    113,
    128,
    133
   ],
   [
    3,
    12,
    84,
    93,
    105,
    125,
    137,
    152
   ],
   [
    4,
    13,
    85,
    86,
    94,
    97,
    106,
    126
   ],
   [
    14,
    49,
    95,
    98,
    127,
    130,
    136,
    156
   ],
   [
    15,
    52,
    86,
    96,
    100,
    115,
    120,
    133
   ],
   [
    5,
    16,
    82,
    86,
    88,
    97,
    112,
    131
   ],
   [
    17,
    55,
    89,
    98,
    123,
    132,
    136,
    157
   ],
   [
    18,
    57,
    87,
    90,
    99,
    105,
    120,
    138
   ],
   [
    6,
    19,
    82,
    83,
    87,
    88,
    100,
    107
   ],
   [
    20,
    60,
    89,
    101,
    108,
    123,
    128,
    141
   ],
   [
    7,
    21,
    84,
    88,
    93,
    102,
    118,
    138
   ],
   [
    8,
    22,
    85,
    89,
    94,
    103,
    119,
    139
   ],
   [
    23,
    62,
    95,
    104,
    130,
    140,
    143,
    160
   ],
   [
    9,
    24,
    83,
    90,
    91,
    105,
    158,
    161
   ],
   [
    25,
    63,
    92,
    106,
    112,
    128,
    131,
    144
   ],
   [
    10,
    26,
    84,
    91,
    93,
    107,
    135,
    151
   ],
   [
    11,
    27,
    85,
    92,
    94,
    96,
    108,
    133
   ],
   [
    28,
    65,
    95,
    109,
    130,
    134,
    146,
    150
   ],
   [
    13,
    29,
    94,
    97,
    110,
    115,
    126,
    144
   ],
   [
    14,
    30,
    95,
    98,
    111,
    116,
    127,
    145
   ],
   [
    31,
    66,
    96,
    99,
    112,
    118,
    133,
    147
   ],
   [
    15,
    32,
    86,
    87,
    96,
    97,
    113,
    120
   ],
   [
    33,
    69,
    98,
    114,
    121,
    136,
    141,
    150
   ],
   [
    16,
    34,
    88,
    97,
    102,
    115,
    131,
    147
   ],
   [
    17,
    35,
    89,
    98,
    103,
    116,
    132,
    148
   ],
   [
    36,
    71,
    104,
    117,
    143,
    149,
    152,
    161
   ],
   [
    18,
    37,
    87,
    99,
    100,
    105,
    118,
    125
   ],
   [
    38,
    72,
    101,
    106,
    119,
    126,
    141,
    153
   ],
   [
    19,
    39,
    83,
    88,
    91,
    100,
    102,
    120
   ],
   [
    20,
    40,
    89,
    92,
    101,
    103,
    121,
    128
   ],
   [
    41,
    74,
    104,
    122,
    129,
    143,
    146,
    155
   ],
   [
    22,
    42,
    94,
    103,
    110,
    123,
    139,
    153
   ],
   [
    23,
    43,
    95,
    104,
    111,
    124,
    140,
    154
   ],
   [
    24,
    44,
    91,
    105,
    107,
    125,
    149,
    161
   ],
   [
    25,
    45,
    92,
    106,
    108,
    126,
    131,
    147
   ],
   [
    46,
    75,
    109,
    127,
    132,
    146,
    148,
    156
   ],
   [
    27,
    47,
    94,
    96,
    108,
    110,
    113,
    128
   ],
   [
    28,
    48,
    95,
    109,
    111,
    114,
    129,
    150
   ],
   [
    30,
    49,
    111,
    116,
    130,
    136,
    145,
    156
   ],
   [
    31,
    50,
    96,
    112,
    113,
    118,
    131,
    138
   ],
   [
    51,
    76,
    114,
    119,
    132,
    139,
    150,
    157
   ],
   [
    32,
    52,
    87,
    97,
    100,
    113,
    115,
    133
   ],
   [
    33,
    53,
    98,
    101,
    114,
    116,
    134,
    141
   ],
   [
    54,
    78,
    117,
    135,
    142,
    152,
    155,
    159
   ],
   [
    35,
    55,
    103,
    116,
    123,
    136,
    148,
    157
   ],
   [
    36,
    56,
    104,
    117,
    124,
    137,
    149,
    158
   ],
   [
    37,
    57,
    90,
    100,
    118,
    120,
    125,
    138
   ],
   [
    38,
    58,
    101,
    119,
    121,
    126,
    139,
    144
   ],
   [
    59,
    79,
    122,
    127,
    140,
    145,
    155,
    160
   ],
   [
    40,
    60,
    92,
    103,
    108,
    121,
    123,
    141
   ],
   [
    41,
    61,
    104,
    109,
    122,
    124,
    142,
    146
   ],
   [
    43,
    62,
    111,
    124,
    130,
    143,
    154,
    160
   ],
   [
    45,
    63,
    108,
    112,
    126,
    128,
    144,
    147
   ],
   [
    46,
    64,
    109,
    127,
    129,
    145,
    148,
    157
   ],
   [
    48,
    65,
    111,
    114,
    129,
    130,
    134,
    146
   ],
   [
    50,
    66,
    99,
    113,
    131,
    133,
    138,
    147
   ],
   [
    51,
    67,
    114,
    132,
    134,
    139,
    148,
    153
   ],
   [
    68,
    80,
    135,
    140,
    149,
    154,
    159,
    161
   ],
   [
    53,
    69,
    101,
    116,
    121,
    134,
    136,
    150
   ],
   [
    54,
    70,
    117,
    122,
    135,
    137,
    151,
    155
   ],
   [
    56,
    71,
    124,
    137,
    143,
    152,
    158,
    161
   ],
   [
    58,
    72,
    106,
    121,
    139,
    141,
    144,
    153
   ],
   [
    59,
    73,
    122,
    140,
    142,
    145,
    154,
    156
   ],
   [
    61,
    74,
    109,
    124,
    129,
    142,
    143,
    155
   ],
   [
    64,
    75,
    129,
    132,
    145,
    146,
    156,
    157
   ],
   [
    67,
    76,
    119,
    134,
    148,
    150,
    153,
    157
   ],
   [
    68,
    77,
    135,
    149,
    151,
    154,
    158,
    160
   ],
   [
    70,
    78,
    122,
    137,
    142,
    151,
    152,
    159
   ],
   [
    73,
    79,
    127,
    142,
    154,
    155,
    156,
    160
   ],
   [
    77,
    80,
    140,
    151,
    158,
    159,
    160,
    161
   ]
  ],
  "Z": [
   [
    0,
    1,
    2,
    3,
    7,
    10,
    81,
    84
   ],
   [
    1,
    5,
    6,
    7,
    16,
    19,
    82,
    88
   ],
   [
    2,
    9,
    10,
    19,
    24,
    39,
    83,
    91
   ],
   [
    3,
    7,
    10,
    12,
    21,
    26,
    84,
    93
   ],
   [
    4,
    8,
    11,
    13,
    22,
    27,
    85,
    94
   ],
   [
    4,
    5,
    13,
    15,
    16,
    32,
    86,
    97
   ],
   [
    6,
    18,
    19,
    32,
    37,
    52,
    87,
    100
   ],
   [
    7,
    16,
    19,
    21,
    34,
    39,
    88,
    102
   ],
   [
    8,
    17,
    20,
    22,
    35,
    40,
    89,
    103
   ],
   [
    0,
    3,
    9,
    18,
    24,
    57,
    90,
    105
   ],
   [
    6,
    10,
    24,
    26,
    39,
    44,
    91,
    107
   ],
   [
    11,
    25,
    27,
    40,
    45,
    60,
    92,
    108
   ],
   [
    0,
    1,
    2,
    12,
    21,
    26,
    81,
    93
   ],
   [
    13,
    22,
    27,
    29,
    42,
    47,
    94,
    110
   ],
   [
    14,
    23,
    28,
    30,
    43,
    48,
    95,
    111
   ],
   [
    15,
    27,
    31,
    32,
    47,
    50,
    96,
    113
   ],
   [
    13,
    16,
    29,
    32,
    34,
    52,
    97,
    115
   ],
   [
    14,
    17,
    30,
    33,
    35,
    53,
    98,
    116
   ],
   [
    1,
    7,
    18,
    31,
    37,
    66,
    99,
    118
   ],
   [
    15,
    19,
    37,
    39,
    52,
    57,
    100,
    120
   ],
   [
    20,
    38,
    40,
    53,
    58,
    69,
    101,
    121
   ],
   [
    1,
    5,
    6,
    21,
    34,
    39,
    82,
    102
   ],
   [
    22,
    35,
    40,
    42,
    55,
    60,
    103,
    123
   ],
   [
    23,
    36,
    41,
    43,
    56,
    61,
    104,
    124
   ],
   [
    3,
    12,
    18,
    24,
    37,
    44,
    105,
    125
   ],
   [
    4,
    13,
    25,
    38,
    45,
    72,
    106,
    126
   ],
   [
    2,
    6,
    9,
    19,
    26,
    44,
    83,
    107
   ],
   [
    20,
    27,
    45,
    47,
    60,
    63,
    108,
    128
   ],
   [
    28,
    46,
    48,
    61,
    64,
    74,
    109,
    129
   ],
   [
    4,
    8,
    11,
    29,
    42,
    47,
    85,
    110
   ],
   [
    30,
    43,
    48,
    49,
    62,
    65,
    111,
    130
   ],
   [
    5,
    16,
    25,
    31,
    50,
    63,
    112,
    131
   ],
   [
    11,
    32,
    47,
    50,
    52,
    66,
    113,
    133
   ],
   [
    33,
    48,
    51,
    53,
    65,
    67,
    114,
    134
   ],
   [
    4,
    5,
    15,
    29,
    34,
    52,
    86,
    115
   ],
   [
    30,
    35,
    49,
    53,
    55,
    69,
    116,
    136
   ],
   [
    0,
    3,
    36,
    54,
    56,
    70,
    117,
    137
   ],
   [
    7,
    21,
    31,
    37,
    50,
    57,
    118,
    138
   ],
   [
    8,
    22,
    38,
    51,
    58,
    76,
    119,
    139
   ],
   [
    6,
    15,
    18,
    32,
    39,
    57,
    87,
    120
   ],
   [
    33,
    40,
    58,
    60,
    69,
    72,
    121,
    141
   ],
   [
    41,
    59,
    61,
    70,
    73,
    78,
    122,
    142
   ],
   [
    8,
    17,
    20,
    42,
    55,
    60,
    89,
    123
   ],
   [
    43,
    56,
    61,
    62,
    71,
    74,
    124,
    143
   ],
   [
    0,
    9,
    12,
    37,
    44,
    57,
    90,
    125
   ],
   [
    13,
    29,
    38,
    45,
    58,
    63,
    126,
    144
   ],
   [
    14,
    30,
    46,
    59,
    64,
    79,
    127,
    145
   ],
   [
    11,
    20,
    25,
    40,
    47,
    63,
    92,
    128
   ],
   [
    41,
    48,
    64,
    65,
    74,
    75,
    129,
    146
   ],
   [
    14,
    23,
    28,
    49,
    62,
    65,
    95,
    130
   ],
   [
    16,
    25,
    34,
    45,
    50,
    66,
    131,
    147
   ],
   [
    17,
    35,
    46,
    51,
    67,
    75,
    132,
    148
   ],
   [
    11,
    15,
    27,
    31,
    52,
    66,
    96,
    133
   ],
   [
    28,
    53,
    65,
    67,
    69,
    76,
    134,
    150
   ],
   [
    10,
    26,
    54,
    68,
    70,
    77,
    135,
    151
   ],
   [
    14,
    17,
    33,
    49,
    55,
    69,
    98,
    136
   ],
   [
    3,
    12,
    56,
    70,
    71,
    78,
    137,
    152
   ],
   [
    1,
    18,
    21,
    50,
    57,
    66,
    99,
    138
   ],
   [
    22,
    42,
    51,
    58,
    67,
    72,
    139,
    153
   ],
   [
    23,
    43,
    59,
    68,
    73,
    80,
    140,
    154
   ],
   [
    20,
    33,
    38,
    53,
    60,
    72,
    101,
    141
   ],
   [
    54,
    61,
    73,
    74,
    78,
    79,
    142,
    155
   ],
   [
    23,
    36,
    41,
    62,
    71,
    74,
    104,
    143
   ],
   [
    4,
    25,
    29,
    58,
    63,
    72,
    106,
    144
   ],
   [
    30,
    49,
    59,
    64,
    73,
    75,
    145,
    156
   ],
   [
    28,
    41,
    46,
    61,
    65,
    75,
    109,
    146
   ],
   [
    5,
    31,
    34,
    45,
    63,
    66,
    112,
    147
   ],
   [
    35,
    46,
    55,
    64,
    67,
    76,
    148,
    157
   ],
   [
    9,
    36,
    44,
    56,
    68,
    77,
    149,
    158
   ],
   [
    28,
    33,
    48,
    51,
    69,
    76,
    114,
    150
   ],
   [
    2,
    26,
    70,
    77,
    78,
    80,
    151,
    159
   ],
   [
    0,
    12,
    36,
    54,
    71,
    78,
    117,
    152
   ],
   [
    8,
    38,
    42,
    67,
    72,
    76,
    119,
    153
   ],
   [
    43,
    62,
    68,
    73,
    77,
    79,
    154,
    160
   ],
   [
    41,
    54,
    59,
    70,
    74,
    79,
    122,
    155
   ],
   [
    14,
    46,
    49,
    73,
    75,
    79,
    127,
    156
   ],
   [
    17,
    51,
    55,
    64,
    75,
    76,
    132,
    157
   ],
   [
    9,
    24,
    56,
    71,
    77,
    80,
    158,
    161
   ],
   [
    2,
    10,
    54,
    68,
    78,
    80,
    135,
    159
   ],
   [
    23,
    59,
    62,
    77,
    79,
    80,
    140,
    160
   ],
   [
    24,
    36,
    44,
    68,
    71,
    80,
    149,
    161
   ]
  ]
 },
 "distance": {
  "d": 3,
  "X": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
    95,
    111,
    130
   ]
  },
  "Z": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
    6,
    19,
    39
   ]
  }
 },
 "provenance": {
  "authors": [
   "@MathysRennela"
  ],
  "construction": "2BGA (arXiv:2306.16400) on SmallGroup(81,3), from github.com/QEC-pages/2BGA-codes @ 403d194c3f98f0cadc236aecbc4a8b6139ccf23c, nonabelian.zip, diswtnonabelian_wt8wtL2_order81_k54.txt, line 1. nonidentity supports a=[4], b=[2, 3, 4, 8, 11].",
  "references": [],
  "date": "2026-09-19",
  "notes": "Literature reproduction of a published 2BGA code (arXiv:2306.16400; github.com/QEC-pages/2BGA-codes @ 403d194c3f98f0cadc236aecbc4a8b6139ccf23c). Checked against the live board: not equivalent to any existing entry.",
  "model": "DeepSeek V4 Flash 0731",
  "origin": "submission"
 },
 "family": "generalized-bicycle"
}