{
 "schema_version": "0.3",
 "name": "[[108,6,16]]",
 "code_type": "CSS",
 "n": 108,
 "k": 6,
 "checks": {
  "X": [
   [
    0,
    2,
    8,
    45,
    54,
    60,
    71,
    87,
    95,
    96
   ],
   [
    1,
    3,
    9,
    44,
    55,
    61,
    70,
    86,
    94,
    97
   ],
   [
    2,
    4,
    10,
    47,
    56,
    62,
    67,
    89,
    91,
    98
   ],
   [
    3,
    5,
    11,
    46,
    57,
    63,
    66,
    88,
    90,
    99
   ],
   [
    0,
    4,
    6,
    43,
    58,
    64,
    69,
    85,
    93,
    100
   ],
   [
    1,
    5,
    7,
    42,
    59,
    65,
    68,
    84,
    92,
    101
   ],
   [
    6,
    8,
    14,
    51,
    59,
    60,
    66,
    75,
    101,
    102
   ],
   [
    7,
    9,
    15,
    50,
    58,
    61,
    67,
    74,
    100,
    103
   ],
   [
    8,
    10,
    16,
    53,
    55,
    62,
    68,
    77,
    97,
    104
   ],
   [
    9,
    11,
    17,
    52,
    54,
    63,
    69,
    76,
    96,
    105
   ],
   [
    6,
    10,
    12,
    49,
    57,
    64,
    70,
    73,
    99,
    106
   ],
   [
    7,
    11,
    13,
    48,
    56,
    65,
    71,
    72,
    98,
    107
   ],
   [
    2,
    12,
    14,
    39,
    54,
    65,
    66,
    81,
    90,
    107
   ],
   [
    3,
    13,
    15,
    38,
    55,
    64,
    67,
    80,
    91,
    106
   ],
   [
    4,
    14,
    16,
    41,
    56,
    61,
    68,
    83,
    92,
    103
   ],
   [
    5,
    15,
    17,
    40,
    57,
    60,
    69,
    82,
    93,
    102
   ],
   [
    0,
    12,
    16,
    37,
    58,
    63,
    70,
    79,
    94,
    105
   ],
   [
    1,
    13,
    17,
    36,
    59,
    62,
    71,
    78,
    95,
    104
   ],
   [
    9,
    18,
    20,
    26,
    59,
    60,
    72,
    78,
    89,
    105
   ],
   [
    8,
    19,
    21,
    27,
    58,
    61,
    73,
    79,
    88,
    104
   ],
   [
    11,
    20,
    22,
    28,
    55,
    62,
    74,
    80,
    85,
    107
   ],
   [
    10,
    21,
    23,
    29,
    54,
    63,
    75,
    81,
    84,
    106
   ],
   [
    7,
    18,
    22,
    24,
    57,
    64,
    76,
    82,
    87,
    103
   ],
   [
    6,
    19,
    23,
    25,
    56,
    65,
    77,
    83,
    86,
    102
   ],
   [
    15,
    24,
    26,
    32,
    65,
    66,
    77,
    78,
    84,
    93
   ],
   [
    14,
    25,
    27,
    33,
    64,
    67,
    76,
    79,
    85,
    92
   ],
   [
    17,
    26,
    28,
    34,
    61,
    68,
    73,
    80,
    86,
    95
   ],
   [
    16,
    27,
    29,
    35,
    60,
    69,
    72,
    81,
    87,
    94
   ],
   [
    13,
    24,
    28,
    30,
    63,
    70,
    75,
    82,
    88,
    91
   ],
   [
    12,
    25,
    29,
    31,
    62,
    71,
    74,
    83,
    89,
    90
   ],
   [
    3,
    20,
    30,
    32,
    54,
    71,
    72,
    83,
    84,
    99
   ],
   [
    2,
    21,
    31,
    33,
    55,
    70,
    73,
    82,
    85,
    98
   ],
   [
    5,
    22,
    32,
    34,
    56,
    67,
    74,
    79,
    86,
    101
   ],
   [
    4,
    23,
    33,
    35,
    57,
    66,
    75,
    78,
    87,
    100
   ],
   [
    1,
    18,
    30,
    34,
    58,
    69,
    76,
    81,
    88,
    97
   ],
   [
    0,
    19,
    31,
    35,
    59,
    68,
    77,
    80,
    89,
    96
   ],
   [
    27,
    36,
    38,
    44,
    69,
    77,
    78,
    90,
    96,
    107
   ],
   [
    26,
    37,
    39,
    45,
    68,
    76,
    79,
    91,
    97,
    106
   ],
   [
    29,
    38,
    40,
    46,
    71,
    73,
    80,
    92,
    98,
    103
   ],
   [
    28,
    39,
    41,
    47,
    70,
    72,
    81,
    93,
    99,
    102
   ],
   [
    25,
    36,
    40,
    42,
    67,
    75,
    82,
    94,
    100,
    105
   ],
   [
    24,
    37,
    41,
    43,
    66,
    74,
    83,
    95,
    101,
    104
   ],
   [
    33,
    42,
    44,
    50,
    57,
    83,
    84,
    95,
    96,
    102
   ],
   [
    32,
    43,
    45,
    51,
    56,
    82,
    85,
    94,
    97,
    103
   ],
   [
    35,
    44,
    46,
    52,
    59,
    79,
    86,
    91,
    98,
    104
   ],
   [
    34,
    45,
    47,
    53,
    58,
    78,
    87,
    90,
    99,
    105
   ],
   [
    31,
    42,
    46,
    48,
    55,
    81,
    88,
    93,
    100,
    106
   ],
   [
    30,
    43,
    47,
    49,
    54,
    80,
    89,
    92,
    101,
    107
   ],
   [
    21,
    38,
    48,
    50,
    63,
    72,
    89,
    90,
    101,
    102
   ],
   [
    20,
    39,
    49,
    51,
    62,
    73,
    88,
    91,
    100,
    103
   ],
   [
    23,
    40,
    50,
    52,
    65,
    74,
    85,
    92,
    97,
    104
   ],
   [
    22,
    41,
    51,
    53,
    64,
    75,
    84,
    93,
    96,
    105
   ],
   [
    19,
    36,
    48,
    52,
    61,
    76,
    87,
    94,
    99,
    106
   ],
   [
    18,
    37,
    49,
    53,
    60,
    77,
    86,
    95,
    98,
    107
   ]
  ],
  "Z": [
   [
    0,
    9,
    12,
    21,
    30,
    47,
    54,
    58,
    70,
    89
   ],
   [
    1,
    8,
    13,
    20,
    31,
    46,
    55,
    59,
    71,
    88
   ],
   [
    2,
    11,
    14,
    23,
    32,
    43,
    54,
    56,
    66,
    85
   ],
   [
    3,
    10,
    15,
    22,
    33,
    42,
    55,
    57,
    67,
    84
   ],
   [
    4,
    7,
    16,
    19,
    34,
    45,
    56,
    58,
    68,
    87
   ],
   [
    5,
    6,
    17,
    18,
    35,
    44,
    57,
    59,
    69,
    86
   ],
   [
    0,
    6,
    15,
    18,
    27,
    53,
    58,
    60,
    64,
    77
   ],
   [
    1,
    7,
    14,
    19,
    26,
    52,
    59,
    61,
    65,
    76
   ],
   [
    2,
    8,
    17,
    20,
    29,
    49,
    54,
    60,
    62,
    73
   ],
   [
    3,
    9,
    16,
    21,
    28,
    48,
    55,
    61,
    63,
    72
   ],
   [
    4,
    10,
    13,
    22,
    25,
    51,
    56,
    62,
    64,
    75
   ],
   [
    5,
    11,
    12,
    23,
    24,
    50,
    57,
    63,
    65,
    74
   ],
   [
    3,
    6,
    12,
    24,
    33,
    41,
    64,
    66,
    70,
    83
   ],
   [
    2,
    7,
    13,
    25,
    32,
    40,
    65,
    67,
    71,
    82
   ],
   [
    5,
    8,
    14,
    26,
    35,
    37,
    60,
    66,
    68,
    79
   ],
   [
    4,
    9,
    15,
    27,
    34,
    36,
    61,
    67,
    69,
    78
   ],
   [
    1,
    10,
    16,
    28,
    31,
    39,
    62,
    68,
    70,
    81
   ],
   [
    0,
    11,
    17,
    29,
    30,
    38,
    63,
    69,
    71,
    80
   ],
   [
    11,
    18,
    27,
    30,
    39,
    48,
    72,
    76,
    88,
    107
   ],
   [
    10,
    19,
    26,
    31,
    38,
    49,
    73,
    77,
    89,
    106
   ],
   [
    7,
    20,
    29,
    32,
    41,
    50,
    72,
    74,
    84,
    103
   ],
   [
    6,
    21,
    28,
    33,
    40,
    51,
    73,
    75,
    85,
    102
   ],
   [
    9,
    22,
    25,
    34,
    37,
    52,
    74,
    76,
    86,
    105
   ],
   [
    8,
    23,
    24,
    35,
    36,
    53,
    75,
    77,
    87,
    104
   ],
   [
    17,
    18,
    24,
    33,
    36,
    45,
    76,
    78,
    82,
    95
   ],
   [
    16,
    19,
    25,
    32,
    37,
    44,
    77,
    79,
    83,
    94
   ],
   [
    13,
    20,
    26,
    35,
    38,
    47,
    72,
    78,
    80,
    91
   ],
   [
    12,
    21,
    27,
    34,
    39,
    46,
    73,
    79,
    81,
    90
   ],
   [
    15,
    22,
    28,
    31,
    40,
    43,
    74,
    80,
    82,
    93
   ],
   [
    14,
    23,
    29,
    30,
    41,
    42,
    75,
    81,
    83,
    92
   ],
   [
    5,
    21,
    24,
    30,
    42,
    51,
    82,
    84,
    88,
    101
   ],
   [
    4,
    20,
    25,
    31,
    43,
    50,
    83,
    85,
    89,
    100
   ],
   [
    1,
    23,
    26,
    32,
    44,
    53,
    78,
    84,
    86,
    97
   ],
   [
    0,
    22,
    27,
    33,
    45,
    52,
    79,
    85,
    87,
    96
   ],
   [
    3,
    19,
    28,
    34,
    46,
    49,
    80,
    86,
    88,
    99
   ],
   [
    2,
    18,
    29,
    35,
    47,
    48,
    81,
    87,
    89,
    98
   ],
   [
    3,
    12,
    29,
    36,
    45,
    48,
    71,
    90,
    94,
    106
   ],
   [
    2,
    13,
    28,
    37,
    44,
    49,
    70,
    91,
    95,
    107
   ],
   [
    5,
    14,
    25,
    38,
    47,
    50,
    67,
    90,
    92,
    102
   ],
   [
    4,
    15,
    24,
    39,
    46,
    51,
    66,
    91,
    93,
    103
   ],
   [
    1,
    16,
    27,
    40,
    43,
    52,
    69,
    92,
    94,
    104
   ],
   [
    0,
    17,
    26,
    41,
    42,
    53,
    68,
    93,
    95,
    105
   ],
   [
    0,
    9,
    35,
    36,
    42,
    51,
    59,
    94,
    96,
    100
   ],
   [
    1,
    8,
    34,
    37,
    43,
    50,
    58,
    95,
    97,
    101
   ],
   [
    2,
    11,
    31,
    38,
    44,
    53,
    55,
    90,
    96,
    98
   ],
   [
    3,
    10,
    30,
    39,
    45,
    52,
    54,
    91,
    97,
    99
   ],
   [
    4,
    7,
    33,
    40,
    46,
    49,
    57,
    92,
    98,
    100
   ],
   [
    5,
    6,
    32,
    41,
    47,
    48,
    56,
    93,
    99,
    101
   ],
   [
    6,
    15,
    23,
    39,
    42,
    48,
    65,
    100,
    102,
    106
   ],
   [
    7,
    14,
    22,
    38,
    43,
    49,
    64,
    101,
    103,
    107
   ],
   [
    8,
    17,
    19,
    41,
    44,
    50,
    61,
    96,
    102,
    104
   ],
   [
    9,
    16,
    18,
    40,
    45,
    51,
    60,
    97,
    103,
    105
   ],
   [
    10,
    13,
    21,
    37,
    46,
    52,
    63,
    98,
    104,
    106
   ],
   [
    11,
    12,
    20,
    36,
    47,
    53,
    62,
    99,
    105,
    107
   ]
  ]
 },
 "distance": {
  "d": 16,
  "X": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": [
    4,
    13,
    15,
    25,
    28,
    35,
    53,
    55,
    62,
    68,
    73,
    81,
    86,
    92,
    94,
    106
   ]
  },
  "Z": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": [
    10,
    15,
    16,
    35,
    52,
    61,
    62,
    69,
    74,
    77,
    86,
    94,
    97,
    100,
    104,
    106
   ]
  }
 },
 "provenance": {
  "authors": [
   "@FarLab"
  ],
  "construction": "2BGA (two-block group algebra) code on group ab(3,3,3,2) (|G|=54); H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T] with a = [0, 4, 16, 35], b = [0, 9, 12, 21, 30, 47] as element indices of the Cayley table (identity = 0; table convention in the note)",
  "origin": "submission",
  "date": "2026-10-17",
  "model": "Claude Opus 5.5",
  "search_budget": {
   "candidates_screened": 26600000,
   "ris_trials_per_side": 30000000,
   "cpu_hours": 3,
   "tool": "research/kit 2BGA sweep + gf2_fast on Brev n2d-highcpu-64"
  }
 },
 "family": "bivariate-bicycle"
}
