{
 "schema_version": "0.1",
 "name": "[[180,36,8]] non-abelian lifted-product (mitten) code",
 "code_type": "CSS",
 "n": 180,
 "k": 36,
 "checks": {
  "X": [
   [
    16,
    27,
    29,
    72,
    88,
    102,
    168,
    171,
    178
   ],
   [
    20,
    23,
    25,
    73,
    92,
    106,
    164,
    175,
    177
   ],
   [
    21,
    22,
    24,
    74,
    93,
    107,
    162,
    175,
    177
   ],
   [
    19,
    21,
    24,
    75,
    96,
    105,
    160,
    173,
    179
   ],
   [
    18,
    20,
    25,
    76,
    97,
    104,
    166,
    173,
    179
   ],
   [
    17,
    26,
    28,
    77,
    89,
    103,
    158,
    171,
    178
   ],
   [
    15,
    17,
    28,
    78,
    100,
    101,
    156,
    169,
    176
   ],
   [
    14,
    16,
    29,
    79,
    100,
    101,
    169,
    170,
    176
   ],
   [
    13,
    30,
    32,
    80,
    85,
    99,
    154,
    167,
    174
   ],
   [
    12,
    31,
    33,
    81,
    84,
    98,
    167,
    172,
    174
   ],
   [
    11,
    13,
    32,
    82,
    97,
    104,
    152,
    165,
    172
   ],
   [
    10,
    12,
    33,
    83,
    96,
    105,
    165,
    172,
    174
   ],
   [
    9,
    34,
    35,
    81,
    84,
    95,
    150,
    163,
    170
   ],
   [
    8,
    34,
    35,
    80,
    85,
    94,
    163,
    170,
    176
   ],
   [
    7,
    9,
    35,
    86,
    93,
    107,
    149,
    161,
    168
   ],
   [
    6,
    8,
    34,
    87,
    92,
    106,
    161,
    168,
    178
   ],
   [
    0,
    31,
    33,
    72,
    88,
    91,
    147,
    159,
    166
   ],
   [
    5,
    30,
    32,
    77,
    89,
    90,
    159,
    166,
    179
   ],
   [
    0,
    4,
    31,
    89,
    90,
    103,
    146,
    157,
    164
   ],
   [
    3,
    5,
    30,
    88,
    91,
    102,
    157,
    164,
    177
   ],
   [
    1,
    27,
    29,
    73,
    87,
    92,
    145,
    155,
    162
   ],
   [
    2,
    26,
    28,
    74,
    86,
    93,
    155,
    162,
    175
   ],
   [
    1,
    2,
    27,
    85,
    94,
    99,
    148,
    153,
    160
   ],
   [
    1,
    2,
    26,
    84,
    95,
    98,
    153,
    160,
    173
   ],
   [
    3,
    23,
    25,
    75,
    83,
    96,
    144,
    151,
    158
   ],
   [
    4,
    22,
    24,
    76,
    82,
    97,
    151,
    158,
    171
   ],
   [
    3,
    5,
    23,
    81,
    95,
    98,
    144,
    151,
    156
   ],
   [
    0,
    4,
    22,
    80,
    94,
    99,
    144,
    156,
    169
   ],
   [
    6,
    19,
    21,
    78,
    79,
    100,
    148,
    153,
    154
   ],
   [
    7,
    18,
    20,
    78,
    79,
    101,
    148,
    154,
    167
   ],
   [
    6,
    8,
    19,
    72,
    91,
    102,
    145,
    152,
    155
   ],
   [
    7,
    9,
    18,
    77,
    90,
    103,
    145,
    152,
    165
   ],
   [
    10,
    15,
    17,
    76,
    82,
    104,
    146,
    150,
    157
   ],
   [
    11,
    14,
    16,
    75,
    83,
    105,
    146,
    150,
    163
   ],
   [
    10,
    12,
    15,
    73,
    87,
    106,
    147,
    149,
    159
   ],
   [
    11,
    13,
    14,
    74,
    86,
    107,
    147,
    149,
    161
   ],
   [
    52,
    63,
    65,
    108,
    124,
    138,
    144,
    152,
    163
   ],
   [
    56,
    59,
    61,
    109,
    128,
    142,
    145,
    149,
    167
   ],
   [
    57,
    58,
    60,
    110,
    129,
    143,
    146,
    147,
    169
   ],
   [
    55,
    57,
    60,
    111,
    132,
    141,
    146,
    147,
    171
   ],
   [
    54,
    56,
    61,
    112,
    133,
    140,
    148,
    150,
    165
   ],
   [
    53,
    62,
    64,
    113,
    125,
    139,
    145,
    149,
    173
   ],
   [
    51,
    53,
    64,
    114,
    136,
    137,
    148,
    150,
    175
   ],
   [
    50,
    52,
    65,
    115,
    136,
    137,
    151,
    154,
    161
   ],
   [
    49,
    66,
    68,
    116,
    121,
    135,
    144,
    152,
    177
   ],
   [
    48,
    67,
    69,
    117,
    120,
    134,
    153,
    156,
    159
   ],
   [
    47,
    49,
    68,
    118,
    133,
    140,
    151,
    154,
    179
   ],
   [
    46,
    48,
    69,
    119,
    132,
    141,
    155,
    157,
    158
   ],
   [
    45,
    70,
    71,
    117,
    120,
    131,
    153,
    156,
    178
   ],
   [
    44,
    70,
    71,
    116,
    121,
    130,
    155,
    157,
    160
   ],
   [
    43,
    45,
    71,
    122,
    129,
    143,
    155,
    158,
    176
   ],
   [
    42,
    44,
    70,
    123,
    128,
    142,
    153,
    159,
    162
   ],
   [
    36,
    67,
    69,
    108,
    124,
    127,
    157,
    160,
    174
   ],
   [
    41,
    66,
    68,
    113,
    125,
    126,
    151,
    161,
    164
   ],
   [
    36,
    40,
    67,
    125,
    126,
    139,
    159,
    162,
    172
   ],
   [
    39,
    41,
    66,
    124,
    127,
    138,
    144,
    163,
    166
   ],
   [
    37,
    63,
    65,
    109,
    123,
    128,
    161,
    164,
    170
   ],
   [
    38,
    62,
    64,
    110,
    122,
    129,
    148,
    165,
    168
   ],
   [
    37,
    38,
    63,
    121,
    130,
    135,
    163,
    166,
    168
   ],
   [
    37,
    38,
    62,
    120,
    131,
    134,
    145,
    167,
    170
   ],
   [
    39,
    59,
    61,
    111,
    119,
    132,
    165,
    166,
    168
   ],
   [
    40,
    58,
    60,
    112,
    118,
    133,
    146,
    169,
    172
   ],
   [
    39,
    41,
    59,
    117,
    131,
    134,
    164,
    167,
    170
   ],
   [
    36,
    40,
    58,
    116,
    130,
    135,
    147,
    171,
    174
   ],
   [
    42,
    55,
    57,
    114,
    115,
    136,
    162,
    169,
    172
   ],
   [
    43,
    54,
    56,
    114,
    115,
    137,
    149,
    173,
    176
   ],
   [
    42,
    44,
    55,
    108,
    127,
    138,
    160,
    171,
    174
   ],
   [
    43,
    45,
    54,
    113,
    126,
    139,
    150,
    175,
    178
   ],
   [
    46,
    51,
    53,
    112,
    118,
    140,
    158,
    173,
    176
   ],
   [
    47,
    50,
    52,
    111,
    119,
    141,
    152,
    177,
    179
   ],
   [
    46,
    48,
    51,
    109,
    123,
    142,
    156,
    175,
    178
   ],
   [
    47,
    49,
    50,
    110,
    122,
    143,
    154,
    177,
    179
   ]
  ],
  "Z": [
   [
    24,
    26,
    27,
    36,
    44,
    55,
    160,
    162,
    171
   ],
   [
    20,
    30,
    31,
    37,
    41,
    59,
    164,
    166,
    167
   ],
   [
    18,
    32,
    33,
    38,
    39,
    61,
    165,
    166,
    167
   ],
   [
    16,
    34,
    35,
    38,
    39,
    63,
    163,
    168,
    170
   ],
   [
    22,
    28,
    29,
    40,
    42,
    57,
    162,
    169,
    171
   ],
   [
    14,
    34,
    35,
    37,
    41,
    65,
    161,
    163,
    170
   ],
   [
    12,
    32,
    33,
    40,
    42,
    67,
    159,
    172,
    174
   ],
   [
    24,
    25,
    26,
    43,
    46,
    53,
    158,
    173,
    175
   ],
   [
    10,
    30,
    31,
    36,
    44,
    69,
    157,
    159,
    174
   ],
   [
    22,
    23,
    28,
    45,
    48,
    51,
    156,
    158,
    175
   ],
   [
    8,
    28,
    29,
    43,
    46,
    71,
    155,
    176,
    178
   ],
   [
    20,
    21,
    30,
    47,
    49,
    50,
    154,
    177,
    179
   ],
   [
    6,
    26,
    27,
    45,
    48,
    70,
    153,
    155,
    178
   ],
   [
    18,
    19,
    32,
    47,
    49,
    52,
    152,
    154,
    179
   ],
   [
    5,
    24,
    25,
    47,
    50,
    68,
    151,
    177,
    179
   ],
   [
    16,
    17,
    34,
    45,
    51,
    54,
    150,
    176,
    178
   ],
   [
    3,
    22,
    23,
    49,
    52,
    66,
    144,
    151,
    177
   ],
   [
    14,
    15,
    35,
    43,
    53,
    56,
    149,
    150,
    176
   ],
   [
    2,
    20,
    21,
    51,
    54,
    64,
    148,
    173,
    175
   ],
   [
    12,
    13,
    33,
    36,
    55,
    58,
    147,
    172,
    174
   ],
   [
    1,
    18,
    19,
    53,
    56,
    62,
    145,
    148,
    173
   ],
   [
    10,
    11,
    31,
    40,
    57,
    60,
    146,
    147,
    172
   ],
   [
    4,
    16,
    17,
    55,
    58,
    60,
    146,
    169,
    171
   ],
   [
    8,
    9,
    29,
    37,
    59,
    62,
    145,
    168,
    170
   ],
   [
    0,
    14,
    15,
    57,
    58,
    60,
    146,
    147,
    169
   ],
   [
    6,
    7,
    27,
    38,
    61,
    64,
    145,
    148,
    168
   ],
   [
    7,
    12,
    13,
    56,
    59,
    62,
    149,
    165,
    167
   ],
   [
    0,
    5,
    25,
    39,
    63,
    66,
    144,
    164,
    166
   ],
   [
    9,
    10,
    11,
    54,
    61,
    64,
    149,
    150,
    165
   ],
   [
    3,
    4,
    23,
    41,
    65,
    68,
    144,
    151,
    164
   ],
   [
    8,
    9,
    11,
    52,
    63,
    66,
    152,
    161,
    163
   ],
   [
    1,
    2,
    21,
    42,
    67,
    70,
    153,
    160,
    162
   ],
   [
    6,
    7,
    13,
    50,
    65,
    68,
    152,
    154,
    161
   ],
   [
    1,
    2,
    19,
    44,
    69,
    71,
    153,
    155,
    160
   ],
   [
    0,
    5,
    15,
    48,
    67,
    70,
    156,
    157,
    159
   ],
   [
    3,
    4,
    17,
    46,
    69,
    71,
    156,
    157,
    158
   ],
   [
    96,
    98,
    99,
    108,
    116,
    127,
    144,
    160,
    174
   ],
   [
    92,
    102,
    103,
    109,
    113,
    131,
    145,
    164,
    178
   ],
   [
    90,
    104,
    105,
    110,
    111,
    133,
    146,
    165,
    179
   ],
   [
    88,
    106,
    107,
    110,
    111,
    135,
    147,
    168,
    177
   ],
   [
    94,
    100,
    101,
    112,
    114,
    129,
    148,
    169,
    176
   ],
   [
    86,
    106,
    107,
    109,
    113,
    137,
    149,
    161,
    175
   ],
   [
    84,
    104,
    105,
    112,
    114,
    139,
    150,
    172,
    173
   ],
   [
    96,
    97,
    98,
    115,
    118,
    125,
    151,
    172,
    173
   ],
   [
    82,
    102,
    103,
    108,
    116,
    141,
    152,
    157,
    171
   ],
   [
    94,
    95,
    100,
    117,
    120,
    123,
    153,
    156,
    170
   ],
   [
    80,
    100,
    101,
    115,
    118,
    143,
    154,
    169,
    176
   ],
   [
    92,
    93,
    102,
    119,
    121,
    122,
    155,
    168,
    177
   ],
   [
    78,
    98,
    99,
    117,
    120,
    142,
    153,
    156,
    167
   ],
   [
    90,
    91,
    104,
    119,
    121,
    124,
    152,
    157,
    166
   ],
   [
    77,
    96,
    97,
    119,
    122,
    140,
    158,
    165,
    179
   ],
   [
    88,
    89,
    106,
    117,
    123,
    126,
    159,
    164,
    178
   ],
   [
    75,
    94,
    95,
    121,
    124,
    138,
    144,
    160,
    163
   ],
   [
    86,
    87,
    107,
    115,
    125,
    128,
    149,
    161,
    162
   ],
   [
    74,
    92,
    93,
    123,
    126,
    136,
    161,
    162,
    175
   ],
   [
    84,
    85,
    105,
    108,
    127,
    130,
    160,
    163,
    174
   ],
   [
    73,
    90,
    91,
    125,
    128,
    134,
    145,
    159,
    164
   ],
   [
    82,
    83,
    103,
    112,
    129,
    132,
    146,
    158,
    165
   ],
   [
    76,
    88,
    89,
    127,
    130,
    132,
    157,
    166,
    171
   ],
   [
    80,
    81,
    101,
    109,
    131,
    134,
    156,
    167,
    170
   ],
   [
    72,
    86,
    87,
    129,
    130,
    132,
    147,
    155,
    168
   ],
   [
    78,
    79,
    99,
    110,
    133,
    136,
    148,
    154,
    169
   ],
   [
    79,
    84,
    85,
    128,
    131,
    134,
    153,
    167,
    170
   ],
   [
    72,
    77,
    97,
    111,
    135,
    138,
    152,
    166,
    171
   ],
   [
    81,
    82,
    83,
    126,
    133,
    136,
    150,
    151,
    172
   ],
   [
    75,
    76,
    95,
    113,
    137,
    140,
    150,
    151,
    173
   ],
   [
    80,
    81,
    83,
    124,
    135,
    138,
    144,
    163,
    174
   ],
   [
    73,
    74,
    93,
    114,
    139,
    142,
    149,
    162,
    175
   ],
   [
    78,
    79,
    85,
    122,
    137,
    140,
    148,
    154,
    176
   ],
   [
    73,
    74,
    91,
    116,
    141,
    143,
    147,
    155,
    177
   ],
   [
    72,
    77,
    87,
    120,
    139,
    142,
    145,
    159,
    178
   ],
   [
    75,
    76,
    89,
    118,
    141,
    143,
    146,
    158,
    179
   ]
  ]
 },
 "distance": {
  "d": 8,
  "X": {
   "value": 8,
   "confidence": "upper_bound",
   "witness": [
    1,
    19,
    23,
    48,
    49,
    50,
    68,
    70
   ]
  },
  "Z": {
   "value": 8,
   "confidence": "upper_bound",
   "witness": [
    3,
    8,
    23,
    27,
    80,
    92,
    99,
    102
   ]
  }
 },
 "provenance": {
  "authors": [
   "@yhu1996"
  ],
  "construction": "Mitten lifted product LP(A,B) (Bhardwaj et al arXiv:2607.28795, Def.4/8) on non-abelian group D18 (order 36): a0=[16, 18, 27], a1=[0, 16, 30], b0=[24, 27, 34], b1=[0, 8, 19] over F2[G]. n=5|G|, k=|G|, weight-9.",
  "references": [
   "arXiv:2607.28795"
  ],
  "date": "2026-08-04",
  "notes": "Found with Jukebox",
  "model": "Claude Opus 4.8"
 },
 "family": "lifted-product"
}