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