{
 "schema_version": "0.1",
 "name": "[[128,64,2]] 2BGA",
 "code_type": "CSS",
 "n": 128,
 "k": 64,
 "checks": {
  "X": [
   [
    0,
    5,
    64,
    69,
    72,
    91,
    100,
    119
   ],
   [
    1,
    10,
    64,
    65,
    69,
    74,
    110,
    124
   ],
   [
    2,
    14,
    64,
    66,
    69,
    78,
    86,
    107
   ],
   [
    3,
    17,
    65,
    67,
    74,
    81,
    117,
    126
   ],
   [
    4,
    19,
    66,
    68,
    78,
    83,
    90,
    112
   ],
   [
    0,
    5,
    64,
    69,
    72,
    91,
    100,
    119
   ],
   [
    6,
    21,
    70,
    77,
    85,
    92,
    99,
    114
   ],
   [
    7,
    24,
    65,
    66,
    71,
    74,
    78,
    88
   ],
   [
    8,
    27,
    67,
    72,
    81,
    91,
    122,
    127
   ],
   [
    9,
    29,
    68,
    71,
    73,
    83,
    88,
    93
   ],
   [
    1,
    10,
    64,
    65,
    69,
    74,
    110,
    124
   ],
   [
    11,
    31,
    70,
    75,
    85,
    87,
    95,
    109
   ],
   [
    12,
    33,
    67,
    71,
    76,
    81,
    88,
    97
   ],
   [
    13,
    35,
    68,
    77,
    83,
    99,
    106,
    121
   ],
   [
    2,
    14,
    64,
    66,
    69,
    78,
    86,
    107
   ],
   [
    15,
    37,
    70,
    79,
    85,
    101,
    108,
    123
   ],
   [
    16,
    38,
    73,
    76,
    80,
    93,
    97,
    102
   ],
   [
    3,
    17,
    65,
    67,
    74,
    81,
    117,
    126
   ],
   [
    18,
    40,
    75,
    82,
    95,
    96,
    104,
    116
   ],
   [
    4,
    19,
    66,
    68,
    78,
    83,
    90,
    112
   ],
   [
    20,
    41,
    79,
    84,
    101,
    105,
    113,
    125
   ],
   [
    6,
    21,
    70,
    77,
    85,
    92,
    99,
    114
   ],
   [
    22,
    43,
    72,
    76,
    86,
    91,
    97,
    107
   ],
   [
    23,
    45,
    73,
    77,
    87,
    93,
    99,
    109
   ],
   [
    7,
    24,
    65,
    66,
    71,
    74,
    78,
    88
   ],
   [
    25,
    47,
    75,
    79,
    89,
    95,
    101,
    111
   ],
   [
    26,
    48,
    80,
    86,
    90,
    102,
    107,
    112
   ],
   [
    8,
    27,
    67,
    72,
    81,
    91,
    122,
    127
   ],
   [
    28,
    50,
    82,
    92,
    104,
    106,
    114,
    121
   ],
   [
    9,
    29,
    68,
    71,
    73,
    83,
    88,
    93
   ],
   [
    30,
    51,
    84,
    89,
    94,
    105,
    111,
    115
   ],
   [
    11,
    31,
    70,
    75,
    85,
    87,
    95,
    109
   ],
   [
    32,
    52,
    80,
    87,
    96,
    102,
    109,
    116
   ],
   [
    12,
    33,
    67,
    71,
    76,
    81,
    88,
    97
   ],
   [
    34,
    54,
    82,
    89,
    98,
    104,
    111,
    118
   ],
   [
    13,
    35,
    68,
    77,
    83,
    99,
    106,
    121
   ],
   [
    36,
    55,
    84,
    100,
    105,
    119,
    122,
    127
   ],
   [
    15,
    37,
    70,
    79,
    85,
    101,
    108,
    123
   ],
   [
    16,
    38,
    73,
    76,
    80,
    93,
    97,
    102
   ],
   [
    39,
    56,
    94,
    98,
    103,
    115,
    118,
    120
   ],
   [
    18,
    40,
    75,
    82,
    95,
    96,
    104,
    116
   ],
   [
    20,
    41,
    79,
    84,
    101,
    105,
    113,
    125
   ],
   [
    42,
    57,
    90,
    96,
    106,
    112,
    116,
    121
   ],
   [
    22,
    43,
    72,
    76,
    86,
    91,
    97,
    107
   ],
   [
    44,
    59,
    92,
    98,
    108,
    114,
    118,
    123
   ],
   [
    23,
    45,
    73,
    77,
    87,
    93,
    99,
    109
   ],
   [
    46,
    60,
    94,
    100,
    110,
    115,
    119,
    124
   ],
   [
    25,
    47,
    75,
    79,
    89,
    95,
    101,
    111
   ],
   [
    26,
    48,
    80,
    86,
    90,
    102,
    107,
    112
   ],
   [
    49,
    61,
    103,
    108,
    113,
    120,
    123,
    125
   ],
   [
    28,
    50,
    82,
    92,
    104,
    106,
    114,
    121
   ],
   [
    30,
    51,
    84,
    89,
    94,
    105,
    111,
    115
   ],
   [
    32,
    52,
    80,
    87,
    96,
    102,
    109,
    116
   ],
   [
    53,
    62,
    103,
    110,
    117,
    120,
    124,
    126
   ],
   [
    34,
    54,
    82,
    89,
    98,
    104,
    111,
    118
   ],
   [
    36,
    55,
    84,
    100,
    105,
    119,
    122,
    127
   ],
   [
    39,
    56,
    94,
    98,
    103,
    115,
    118,
    120
   ],
   [
    42,
    57,
    90,
    96,
    106,
    112,
    116,
    121
   ],
   [
    58,
    63,
    113,
    117,
    122,
    125,
    126,
    127
   ],
   [
    44,
    59,
    92,
    98,
    108,
    114,
    118,
    123
   ],
   [
    46,
    60,
    94,
    100,
    110,
    115,
    119,
    124
   ],
   [
    49,
    61,
    103,
    108,
    113,
    120,
    123,
    125
   ],
   [
    53,
    62,
    103,
    110,
    117,
    120,
    124,
    126
   ],
   [
    58,
    63,
    113,
    117,
    122,
    125,
    126,
    127
   ]
  ],
  "Z": [
   [
    0,
    1,
    2,
    5,
    10,
    14,
    64,
    69
   ],
   [
    1,
    3,
    7,
    10,
    17,
    24,
    65,
    74
   ],
   [
    2,
    4,
    7,
    14,
    19,
    24,
    66,
    78
   ],
   [
    3,
    8,
    12,
    17,
    27,
    33,
    67,
    81
   ],
   [
    4,
    9,
    13,
    19,
    29,
    35,
    68,
    83
   ],
   [
    0,
    1,
    2,
    5,
    10,
    14,
    64,
    69
   ],
   [
    6,
    11,
    15,
    21,
    31,
    37,
    70,
    85
   ],
   [
    7,
    9,
    12,
    24,
    29,
    33,
    71,
    88
   ],
   [
    0,
    5,
    8,
    22,
    27,
    43,
    72,
    91
   ],
   [
    9,
    16,
    23,
    29,
    38,
    45,
    73,
    93
   ],
   [
    1,
    3,
    7,
    10,
    17,
    24,
    65,
    74
   ],
   [
    11,
    18,
    25,
    31,
    40,
    47,
    75,
    95
   ],
   [
    12,
    16,
    22,
    33,
    38,
    43,
    76,
    97
   ],
   [
    6,
    13,
    21,
    23,
    35,
    45,
    77,
    99
   ],
   [
    2,
    4,
    7,
    14,
    19,
    24,
    66,
    78
   ],
   [
    15,
    20,
    25,
    37,
    41,
    47,
    79,
    101
   ],
   [
    16,
    26,
    32,
    38,
    48,
    52,
    80,
    102
   ],
   [
    3,
    8,
    12,
    17,
    27,
    33,
    67,
    81
   ],
   [
    18,
    28,
    34,
    40,
    50,
    54,
    82,
    104
   ],
   [
    4,
    9,
    13,
    19,
    29,
    35,
    68,
    83
   ],
   [
    20,
    30,
    36,
    41,
    51,
    55,
    84,
    105
   ],
   [
    6,
    11,
    15,
    21,
    31,
    37,
    70,
    85
   ],
   [
    2,
    14,
    22,
    26,
    43,
    48,
    86,
    107
   ],
   [
    11,
    23,
    31,
    32,
    45,
    52,
    87,
    109
   ],
   [
    7,
    9,
    12,
    24,
    29,
    33,
    71,
    88
   ],
   [
    25,
    30,
    34,
    47,
    51,
    54,
    89,
    111
   ],
   [
    4,
    19,
    26,
    42,
    48,
    57,
    90,
    112
   ],
   [
    0,
    5,
    8,
    22,
    27,
    43,
    72,
    91
   ],
   [
    6,
    21,
    28,
    44,
    50,
    59,
    92,
    114
   ],
   [
    9,
    16,
    23,
    29,
    38,
    45,
    73,
    93
   ],
   [
    30,
    39,
    46,
    51,
    56,
    60,
    94,
    115
   ],
   [
    11,
    18,
    25,
    31,
    40,
    47,
    75,
    95
   ],
   [
    18,
    32,
    40,
    42,
    52,
    57,
    96,
    116
   ],
   [
    12,
    16,
    22,
    33,
    38,
    43,
    76,
    97
   ],
   [
    34,
    39,
    44,
    54,
    56,
    59,
    98,
    118
   ],
   [
    6,
    13,
    21,
    23,
    35,
    45,
    77,
    99
   ],
   [
    0,
    5,
    36,
    46,
    55,
    60,
    100,
    119
   ],
   [
    15,
    20,
    25,
    37,
    41,
    47,
    79,
    101
   ],
   [
    16,
    26,
    32,
    38,
    48,
    52,
    80,
    102
   ],
   [
    39,
    49,
    53,
    56,
    61,
    62,
    103,
    120
   ],
   [
    18,
    28,
    34,
    40,
    50,
    54,
    82,
    104
   ],
   [
    20,
    30,
    36,
    41,
    51,
    55,
    84,
    105
   ],
   [
    13,
    28,
    35,
    42,
    50,
    57,
    106,
    121
   ],
   [
    2,
    14,
    22,
    26,
    43,
    48,
    86,
    107
   ],
   [
    15,
    37,
    44,
    49,
    59,
    61,
    108,
    123
   ],
   [
    11,
    23,
    31,
    32,
    45,
    52,
    87,
    109
   ],
   [
    1,
    10,
    46,
    53,
    60,
    62,
    110,
    124
   ],
   [
    25,
    30,
    34,
    47,
    51,
    54,
    89,
    111
   ],
   [
    4,
    19,
    26,
    42,
    48,
    57,
    90,
    112
   ],
   [
    20,
    41,
    49,
    58,
    61,
    63,
    113,
    125
   ],
   [
    6,
    21,
    28,
    44,
    50,
    59,
    92,
    114
   ],
   [
    30,
    39,
    46,
    51,
    56,
    60,
    94,
    115
   ],
   [
    18,
    32,
    40,
    42,
    52,
    57,
    96,
    116
   ],
   [
    3,
    17,
    53,
    58,
    62,
    63,
    117,
    126
   ],
   [
    34,
    39,
    44,
    54,
    56,
    59,
    98,
    118
   ],
   [
    0,
    5,
    36,
    46,
    55,
    60,
    100,
    119
   ],
   [
    39,
    49,
    53,
    56,
    61,
    62,
    103,
    120
   ],
   [
    13,
    28,
    35,
    42,
    50,
    57,
    106,
    121
   ],
   [
    8,
    27,
    36,
    55,
    58,
    63,
    122,
    127
   ],
   [
    15,
    37,
    44,
    49,
    59,
    61,
    108,
    123
   ],
   [
    1,
    10,
    46,
    53,
    60,
    62,
    110,
    124
   ],
   [
    20,
    41,
    49,
    58,
    61,
    63,
    113,
    125
   ],
   [
    3,
    17,
    53,
    58,
    62,
    63,
    117,
    126
   ],
   [
    8,
    27,
    36,
    55,
    58,
    63,
    122,
    127
   ]
  ]
 },
 "distance": {
  "d": 2,
  "X": {
   "value": 2,
   "confidence": "upper_bound",
   "witness": [
    11,
    31
   ]
  },
  "Z": {
   "value": 2,
   "confidence": "upper_bound",
   "witness": [
    9,
    29
   ]
  }
 },
 "provenance": {
  "authors": [
   "@MathysRennela"
  ],
  "construction": "2BGA (arXiv:2306.16400) on SmallGroup(64,3), from github.com/QEC-pages/2BGA-codes @ 403d194c3f98f0cadc236aecbc4a8b6139ccf23c, nonabelian.zip, diswtnonabelian_wt8wtL2_order64_k64.txt, line 1. nonidentity supports a=[6], b=[2, 3, 6, 11, 15].",
  "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"
}