{
 "schema_version": "0.1",
 "name": "[[144,16,12]]",
 "code_type": "CSS",
 "n": 144,
 "k": 16,
 "checks": {
  "X": [
   [
    0,
    5,
    55,
    72,
    98,
    106,
    110,
    143
   ],
   [
    0,
    1,
    56,
    73,
    99,
    107,
    111,
    138
   ],
   [
    1,
    2,
    57,
    74,
    100,
    102,
    112,
    139
   ],
   [
    2,
    3,
    58,
    75,
    101,
    103,
    113,
    140
   ],
   [
    3,
    4,
    59,
    76,
    96,
    104,
    108,
    141
   ],
   [
    4,
    5,
    54,
    77,
    97,
    105,
    109,
    142
   ],
   [
    6,
    11,
    61,
    77,
    78,
    104,
    112,
    116
   ],
   [
    6,
    7,
    62,
    72,
    79,
    105,
    113,
    117
   ],
   [
    7,
    8,
    63,
    73,
    80,
    106,
    108,
    118
   ],
   [
    8,
    9,
    64,
    74,
    81,
    107,
    109,
    119
   ],
   [
    9,
    10,
    65,
    75,
    82,
    102,
    110,
    114
   ],
   [
    10,
    11,
    60,
    76,
    83,
    103,
    111,
    115
   ],
   [
    12,
    17,
    67,
    83,
    84,
    110,
    118,
    122
   ],
   [
    12,
    13,
    68,
    78,
    85,
    111,
    119,
    123
   ],
   [
    13,
    14,
    69,
    79,
    86,
    112,
    114,
    124
   ],
   [
    14,
    15,
    70,
    80,
    87,
    113,
    115,
    125
   ],
   [
    15,
    16,
    71,
    81,
    88,
    108,
    116,
    120
   ],
   [
    16,
    17,
    66,
    82,
    89,
    109,
    117,
    121
   ],
   [
    1,
    18,
    23,
    89,
    90,
    116,
    124,
    128
   ],
   [
    2,
    18,
    19,
    84,
    91,
    117,
    125,
    129
   ],
   [
    3,
    19,
    20,
    85,
    92,
    118,
    120,
    130
   ],
   [
    4,
    20,
    21,
    86,
    93,
    119,
    121,
    131
   ],
   [
    5,
    21,
    22,
    87,
    94,
    114,
    122,
    126
   ],
   [
    0,
    22,
    23,
    88,
    95,
    115,
    123,
    127
   ],
   [
    7,
    24,
    29,
    95,
    96,
    122,
    130,
    134
   ],
   [
    8,
    24,
    25,
    90,
    97,
    123,
    131,
    135
   ],
   [
    9,
    25,
    26,
    91,
    98,
    124,
    126,
    136
   ],
   [
    10,
    26,
    27,
    92,
    99,
    125,
    127,
    137
   ],
   [
    11,
    27,
    28,
    93,
    100,
    120,
    128,
    132
   ],
   [
    6,
    28,
    29,
    94,
    101,
    121,
    129,
    133
   ],
   [
    13,
    30,
    35,
    101,
    102,
    128,
    136,
    140
   ],
   [
    14,
    30,
    31,
    96,
    103,
    129,
    137,
    141
   ],
   [
    15,
    31,
    32,
    97,
    104,
    130,
    132,
    142
   ],
   [
    16,
    32,
    33,
    98,
    105,
    131,
    133,
    143
   ],
   [
    17,
    33,
    34,
    99,
    106,
    126,
    134,
    138
   ],
   [
    12,
    34,
    35,
    100,
    107,
    127,
    135,
    139
   ],
   [
    19,
    36,
    41,
    74,
    107,
    108,
    134,
    142
   ],
   [
    20,
    36,
    37,
    75,
    102,
    109,
    135,
    143
   ],
   [
    21,
    37,
    38,
    76,
    103,
    110,
    136,
    138
   ],
   [
    22,
    38,
    39,
    77,
    104,
    111,
    137,
    139
   ],
   [
    23,
    39,
    40,
    72,
    105,
    112,
    132,
    140
   ],
   [
    18,
    40,
    41,
    73,
    106,
    113,
    133,
    141
   ],
   [
    25,
    42,
    47,
    76,
    80,
    113,
    114,
    140
   ],
   [
    26,
    42,
    43,
    77,
    81,
    108,
    115,
    141
   ],
   [
    27,
    43,
    44,
    72,
    82,
    109,
    116,
    142
   ],
   [
    28,
    44,
    45,
    73,
    83,
    110,
    117,
    143
   ],
   [
    29,
    45,
    46,
    74,
    78,
    111,
    118,
    138
   ],
   [
    24,
    46,
    47,
    75,
    79,
    112,
    119,
    139
   ],
   [
    31,
    48,
    53,
    74,
    82,
    86,
    119,
    120
   ],
   [
    32,
    48,
    49,
    75,
    83,
    87,
    114,
    121
   ],
   [
    33,
    49,
    50,
    76,
    78,
    88,
    115,
    122
   ],
   [
    34,
    50,
    51,
    77,
    79,
    89,
    116,
    123
   ],
   [
    35,
    51,
    52,
    72,
    80,
    84,
    117,
    124
   ],
   [
    30,
    52,
    53,
    73,
    81,
    85,
    118,
    125
   ],
   [
    37,
    54,
    59,
    80,
    88,
    92,
    125,
    126
   ],
   [
    38,
    54,
    55,
    81,
    89,
    93,
    120,
    127
   ],
   [
    39,
    55,
    56,
    82,
    84,
    94,
    121,
    128
   ],
   [
    40,
    56,
    57,
    83,
    85,
    95,
    122,
    129
   ],
   [
    41,
    57,
    58,
    78,
    86,
    90,
    123,
    130
   ],
   [
    36,
    58,
    59,
    79,
    87,
    91,
    124,
    131
   ],
   [
    43,
    60,
    65,
    86,
    94,
    98,
    131,
    132
   ],
   [
    44,
    60,
    61,
    87,
    95,
    99,
    126,
    133
   ],
   [
    45,
    61,
    62,
    88,
    90,
    100,
    127,
    134
   ],
   [
    46,
    62,
    63,
    89,
    91,
    101,
    128,
    135
   ],
   [
    47,
    63,
    64,
    84,
    92,
    96,
    129,
    136
   ],
   [
    42,
    64,
    65,
    85,
    93,
    97,
    130,
    137
   ],
   [
    49,
    66,
    71,
    92,
    100,
    104,
    137,
    138
   ],
   [
    50,
    66,
    67,
    93,
    101,
    105,
    132,
    139
   ],
   [
    51,
    67,
    68,
    94,
    96,
    106,
    133,
    140
   ],
   [
    52,
    68,
    69,
    95,
    97,
    107,
    134,
    141
   ],
   [
    53,
    69,
    70,
    90,
    98,
    102,
    135,
    142
   ],
   [
    48,
    70,
    71,
    91,
    99,
    103,
    136,
    143
   ]
  ],
  "Z": [
   [
    0,
    7,
    40,
    44,
    52,
    72,
    73,
    95
   ],
   [
    1,
    8,
    41,
    45,
    53,
    73,
    74,
    90
   ],
   [
    2,
    9,
    36,
    46,
    48,
    74,
    75,
    91
   ],
   [
    3,
    10,
    37,
    47,
    49,
    75,
    76,
    92
   ],
   [
    4,
    11,
    38,
    42,
    50,
    76,
    77,
    93
   ],
   [
    5,
    6,
    39,
    43,
    51,
    72,
    77,
    94
   ],
   [
    6,
    13,
    46,
    50,
    58,
    78,
    79,
    101
   ],
   [
    7,
    14,
    47,
    51,
    59,
    79,
    80,
    96
   ],
   [
    8,
    15,
    42,
    52,
    54,
    80,
    81,
    97
   ],
   [
    9,
    16,
    43,
    53,
    55,
    81,
    82,
    98
   ],
   [
    10,
    17,
    44,
    48,
    56,
    82,
    83,
    99
   ],
   [
    11,
    12,
    45,
    49,
    57,
    78,
    83,
    100
   ],
   [
    12,
    19,
    52,
    56,
    64,
    84,
    85,
    107
   ],
   [
    13,
    20,
    53,
    57,
    65,
    85,
    86,
    102
   ],
   [
    14,
    21,
    48,
    58,
    60,
    86,
    87,
    103
   ],
   [
    15,
    22,
    49,
    59,
    61,
    87,
    88,
    104
   ],
   [
    16,
    23,
    50,
    54,
    62,
    88,
    89,
    105
   ],
   [
    17,
    18,
    51,
    55,
    63,
    84,
    89,
    106
   ],
   [
    18,
    25,
    58,
    62,
    70,
    90,
    91,
    113
   ],
   [
    19,
    26,
    59,
    63,
    71,
    91,
    92,
    108
   ],
   [
    20,
    27,
    54,
    64,
    66,
    92,
    93,
    109
   ],
   [
    21,
    28,
    55,
    65,
    67,
    93,
    94,
    110
   ],
   [
    22,
    29,
    56,
    60,
    68,
    94,
    95,
    111
   ],
   [
    23,
    24,
    57,
    61,
    69,
    90,
    95,
    112
   ],
   [
    4,
    24,
    31,
    64,
    68,
    96,
    97,
    119
   ],
   [
    5,
    25,
    32,
    65,
    69,
    97,
    98,
    114
   ],
   [
    0,
    26,
    33,
    60,
    70,
    98,
    99,
    115
   ],
   [
    1,
    27,
    34,
    61,
    71,
    99,
    100,
    116
   ],
   [
    2,
    28,
    35,
    62,
    66,
    100,
    101,
    117
   ],
   [
    3,
    29,
    30,
    63,
    67,
    96,
    101,
    118
   ],
   [
    2,
    10,
    30,
    37,
    70,
    102,
    103,
    125
   ],
   [
    3,
    11,
    31,
    38,
    71,
    103,
    104,
    120
   ],
   [
    4,
    6,
    32,
    39,
    66,
    104,
    105,
    121
   ],
   [
    5,
    7,
    33,
    40,
    67,
    105,
    106,
    122
   ],
   [
    0,
    8,
    34,
    41,
    68,
    106,
    107,
    123
   ],
   [
    1,
    9,
    35,
    36,
    69,
    102,
    107,
    124
   ],
   [
    4,
    8,
    16,
    36,
    43,
    108,
    109,
    131
   ],
   [
    5,
    9,
    17,
    37,
    44,
    109,
    110,
    126
   ],
   [
    0,
    10,
    12,
    38,
    45,
    110,
    111,
    127
   ],
   [
    1,
    11,
    13,
    39,
    46,
    111,
    112,
    128
   ],
   [
    2,
    6,
    14,
    40,
    47,
    112,
    113,
    129
   ],
   [
    3,
    7,
    15,
    41,
    42,
    108,
    113,
    130
   ],
   [
    10,
    14,
    22,
    42,
    49,
    114,
    115,
    137
   ],
   [
    11,
    15,
    23,
    43,
    50,
    115,
    116,
    132
   ],
   [
    6,
    16,
    18,
    44,
    51,
    116,
    117,
    133
   ],
   [
    7,
    17,
    19,
    45,
    52,
    117,
    118,
    134
   ],
   [
    8,
    12,
    20,
    46,
    53,
    118,
    119,
    135
   ],
   [
    9,
    13,
    21,
    47,
    48,
    114,
    119,
    136
   ],
   [
    16,
    20,
    28,
    48,
    55,
    120,
    121,
    143
   ],
   [
    17,
    21,
    29,
    49,
    56,
    121,
    122,
    138
   ],
   [
    12,
    22,
    24,
    50,
    57,
    122,
    123,
    139
   ],
   [
    13,
    23,
    25,
    51,
    58,
    123,
    124,
    140
   ],
   [
    14,
    18,
    26,
    52,
    59,
    124,
    125,
    141
   ],
   [
    15,
    19,
    27,
    53,
    54,
    120,
    125,
    142
   ],
   [
    22,
    26,
    34,
    54,
    61,
    77,
    126,
    127
   ],
   [
    23,
    27,
    35,
    55,
    62,
    72,
    127,
    128
   ],
   [
    18,
    28,
    30,
    56,
    63,
    73,
    128,
    129
   ],
   [
    19,
    29,
    31,
    57,
    64,
    74,
    129,
    130
   ],
   [
    20,
    24,
    32,
    58,
    65,
    75,
    130,
    131
   ],
   [
    21,
    25,
    33,
    59,
    60,
    76,
    126,
    131
   ],
   [
    28,
    32,
    40,
    60,
    67,
    83,
    132,
    133
   ],
   [
    29,
    33,
    41,
    61,
    68,
    78,
    133,
    134
   ],
   [
    24,
    34,
    36,
    62,
    69,
    79,
    134,
    135
   ],
   [
    25,
    35,
    37,
    63,
    70,
    80,
    135,
    136
   ],
   [
    26,
    30,
    38,
    64,
    71,
    81,
    136,
    137
   ],
   [
    27,
    31,
    39,
    65,
    66,
    82,
    132,
    137
   ],
   [
    1,
    34,
    38,
    46,
    66,
    89,
    138,
    139
   ],
   [
    2,
    35,
    39,
    47,
    67,
    84,
    139,
    140
   ],
   [
    3,
    30,
    40,
    42,
    68,
    85,
    140,
    141
   ],
   [
    4,
    31,
    41,
    43,
    69,
    86,
    141,
    142
   ],
   [
    5,
    32,
    36,
    44,
    70,
    87,
    142,
    143
   ],
   [
    0,
    33,
    37,
    45,
    71,
    88,
    138,
    143
   ]
  ]
 },
 "distance": {
  "d": 12,
  "X": {
   "value": 12,
   "confidence": "upper_bound",
   "witness": [
    12,
    20,
    21,
    48,
    56,
    57,
    75,
    76,
    93,
    111,
    112,
    129
   ]
  },
  "Z": {
   "value": 12,
   "confidence": "upper_bound",
   "witness": [
    10,
    11,
    29,
    46,
    47,
    65,
    96,
    101,
    104,
    132,
    137,
    140
   ]
  }
 },
 "provenance": {
  "authors": [
   "@MathysRennela"
  ],
  "construction": "Bivariate bicycle code QC(A,B) on Z_12 x Z_6 with asymmetric weight-3+5 generators A = 1 + y^5 + x^9 y, B = 1 + x^4 y^2 + x^5 y^4 + x^6 y^2 + x^11 y^5 (weight-8 checks). Found by a weight-8 gap sweep that extended arXiv:2609.06572's family to unbalanced generator weights.",
  "origin": "submission",
  "date": "2026-09-09",
  "model": "Omen Alpha 1.0",
  "notes": "New parameters (submitter claim). Distance: RIS upper bound d<=12 (20k trials), corroborated by BP+OSD at 200k trials/side (weight-12 logicals, nothing lighter); exact certification not run.",
  "novelty": "new_parameters"
 },
 "family": "bivariate-bicycle"
}