{
 "schema_version": "0.1",
 "name": "[[216,8,21]]",
 "code_type": "CSS",
 "n": 216,
 "k": 8,
 "checks": {
  "X": [
   [
    15,
    55,
    72,
    100,
    123,
    192,
    196,
    209
   ],
   [
    12,
    52,
    73,
    101,
    120,
    193,
    197,
    210
   ],
   [
    13,
    53,
    74,
    102,
    121,
    194,
    198,
    211
   ],
   [
    14,
    54,
    75,
    103,
    122,
    195,
    199,
    208
   ],
   [
    19,
    59,
    76,
    104,
    127,
    196,
    200,
    213
   ],
   [
    16,
    56,
    77,
    105,
    124,
    197,
    201,
    214
   ],
   [
    17,
    57,
    78,
    106,
    125,
    198,
    202,
    215
   ],
   [
    18,
    58,
    79,
    107,
    126,
    199,
    203,
    212
   ],
   [
    0,
    23,
    63,
    80,
    109,
    131,
    200,
    204
   ],
   [
    1,
    20,
    60,
    81,
    110,
    128,
    201,
    205
   ],
   [
    2,
    21,
    61,
    82,
    111,
    129,
    202,
    206
   ],
   [
    3,
    22,
    62,
    83,
    108,
    130,
    203,
    207
   ],
   [
    4,
    27,
    67,
    84,
    113,
    135,
    204,
    208
   ],
   [
    5,
    24,
    64,
    85,
    114,
    132,
    205,
    209
   ],
   [
    6,
    25,
    65,
    86,
    115,
    133,
    206,
    210
   ],
   [
    7,
    26,
    66,
    87,
    112,
    134,
    207,
    211
   ],
   [
    8,
    31,
    71,
    88,
    117,
    139,
    208,
    212
   ],
   [
    9,
    28,
    68,
    89,
    118,
    136,
    209,
    213
   ],
   [
    10,
    29,
    69,
    90,
    119,
    137,
    210,
    214
   ],
   [
    11,
    30,
    70,
    91,
    116,
    138,
    211,
    215
   ],
   [
    12,
    35,
    75,
    92,
    108,
    121,
    143,
    212
   ],
   [
    13,
    32,
    72,
    93,
    109,
    122,
    140,
    213
   ],
   [
    14,
    33,
    73,
    94,
    110,
    123,
    141,
    214
   ],
   [
    15,
    34,
    74,
    95,
    111,
    120,
    142,
    215
   ],
   [
    16,
    39,
    79,
    96,
    108,
    112,
    125,
    147
   ],
   [
    17,
    36,
    76,
    97,
    109,
    113,
    126,
    144
   ],
   [
    18,
    37,
    77,
    98,
    110,
    114,
    127,
    145
   ],
   [
    19,
    38,
    78,
    99,
    111,
    115,
    124,
    146
   ],
   [
    20,
    43,
    83,
    100,
    112,
    116,
    129,
    151
   ],
   [
    21,
    40,
    80,
    101,
    113,
    117,
    130,
    148
   ],
   [
    22,
    41,
    81,
    102,
    114,
    118,
    131,
    149
   ],
   [
    23,
    42,
    82,
    103,
    115,
    119,
    128,
    150
   ],
   [
    24,
    47,
    87,
    104,
    116,
    120,
    133,
    155
   ],
   [
    25,
    44,
    84,
    105,
    117,
    121,
    134,
    152
   ],
   [
    26,
    45,
    85,
    106,
    118,
    122,
    135,
    153
   ],
   [
    27,
    46,
    86,
    107,
    119,
    123,
    132,
    154
   ],
   [
    0,
    28,
    51,
    91,
    120,
    124,
    137,
    159
   ],
   [
    1,
    29,
    48,
    88,
    121,
    125,
    138,
    156
   ],
   [
    2,
    30,
    49,
    89,
    122,
    126,
    139,
    157
   ],
   [
    3,
    31,
    50,
    90,
    123,
    127,
    136,
    158
   ],
   [
    4,
    32,
    55,
    95,
    124,
    128,
    141,
    163
   ],
   [
    5,
    33,
    52,
    92,
    125,
    129,
    142,
    160
   ],
   [
    6,
    34,
    53,
    93,
    126,
    130,
    143,
    161
   ],
   [
    7,
    35,
    54,
    94,
    127,
    131,
    140,
    162
   ],
   [
    8,
    36,
    59,
    99,
    128,
    132,
    145,
    167
   ],
   [
    9,
    37,
    56,
    96,
    129,
    133,
    146,
    164
   ],
   [
    10,
    38,
    57,
    97,
    130,
    134,
    147,
    165
   ],
   [
    11,
    39,
    58,
    98,
    131,
    135,
    144,
    166
   ],
   [
    12,
    40,
    63,
    103,
    132,
    136,
    149,
    171
   ],
   [
    13,
    41,
    60,
    100,
    133,
    137,
    150,
    168
   ],
   [
    14,
    42,
    61,
    101,
    134,
    138,
    151,
    169
   ],
   [
    15,
    43,
    62,
    102,
    135,
    139,
    148,
    170
   ],
   [
    16,
    44,
    67,
    107,
    136,
    140,
    153,
    175
   ],
   [
    17,
    45,
    64,
    104,
    137,
    141,
    154,
    172
   ],
   [
    18,
    46,
    65,
    105,
    138,
    142,
    155,
    173
   ],
   [
    19,
    47,
    66,
    106,
    139,
    143,
    152,
    174
   ],
   [
    3,
    20,
    48,
    71,
    140,
    144,
    157,
    179
   ],
   [
    0,
    21,
    49,
    68,
    141,
    145,
    158,
    176
   ],
   [
    1,
    22,
    50,
    69,
    142,
    146,
    159,
    177
   ],
   [
    2,
    23,
    51,
    70,
    143,
    147,
    156,
    178
   ],
   [
    7,
    24,
    52,
    75,
    144,
    148,
    161,
    183
   ],
   [
    4,
    25,
    53,
    72,
    145,
    149,
    162,
    180
   ],
   [
    5,
    26,
    54,
    73,
    146,
    150,
    163,
    181
   ],
   [
    6,
    27,
    55,
    74,
    147,
    151,
    160,
    182
   ],
   [
    11,
    28,
    56,
    79,
    148,
    152,
    165,
    187
   ],
   [
    8,
    29,
    57,
    76,
    149,
    153,
    166,
    184
   ],
   [
    9,
    30,
    58,
    77,
    150,
    154,
    167,
    185
   ],
   [
    10,
    31,
    59,
    78,
    151,
    155,
    164,
    186
   ],
   [
    15,
    32,
    60,
    83,
    152,
    156,
    169,
    191
   ],
   [
    12,
    33,
    61,
    80,
    153,
    157,
    170,
    188
   ],
   [
    13,
    34,
    62,
    81,
    154,
    158,
    171,
    189
   ],
   [
    14,
    35,
    63,
    82,
    155,
    159,
    168,
    190
   ],
   [
    19,
    36,
    64,
    87,
    156,
    160,
    173,
    195
   ],
   [
    16,
    37,
    65,
    84,
    157,
    161,
    174,
    192
   ],
   [
    17,
    38,
    66,
    85,
    158,
    162,
    175,
    193
   ],
   [
    18,
    39,
    67,
    86,
    159,
    163,
    172,
    194
   ],
   [
    23,
    40,
    68,
    91,
    160,
    164,
    177,
    199
   ],
   [
    20,
    41,
    69,
    88,
    161,
    165,
    178,
    196
   ],
   [
    21,
    42,
    70,
    89,
    162,
    166,
    179,
    197
   ],
   [
    22,
    43,
    71,
    90,
    163,
    167,
    176,
    198
   ],
   [
    27,
    44,
    72,
    95,
    164,
    168,
    181,
    203
   ],
   [
    24,
    45,
    73,
    92,
    165,
    169,
    182,
    200
   ],
   [
    25,
    46,
    74,
    93,
    166,
    170,
    183,
    201
   ],
   [
    26,
    47,
    75,
    94,
    167,
    171,
    180,
    202
   ],
   [
    31,
    48,
    76,
    99,
    168,
    172,
    185,
    207
   ],
   [
    28,
    49,
    77,
    96,
    169,
    173,
    186,
    204
   ],
   [
    29,
    50,
    78,
    97,
    170,
    174,
    187,
    205
   ],
   [
    30,
    51,
    79,
    98,
    171,
    175,
    184,
    206
   ],
   [
    35,
    52,
    80,
    103,
    172,
    176,
    189,
    211
   ],
   [
    32,
    53,
    81,
    100,
    173,
    177,
    190,
    208
   ],
   [
    33,
    54,
    82,
    101,
    174,
    178,
    191,
    209
   ],
   [
    34,
    55,
    83,
    102,
    175,
    179,
    188,
    210
   ],
   [
    39,
    56,
    84,
    107,
    176,
    180,
    193,
    215
   ],
   [
    36,
    57,
    85,
    104,
    177,
    181,
    194,
    212
   ],
   [
    37,
    58,
    86,
    105,
    178,
    182,
    195,
    213
   ],
   [
    38,
    59,
    87,
    106,
    179,
    183,
    192,
    214
   ],
   [
    3,
    43,
    60,
    88,
    111,
    180,
    184,
    197
   ],
   [
    0,
    40,
    61,
    89,
    108,
    181,
    185,
    198
   ],
   [
    1,
    41,
    62,
    90,
    109,
    182,
    186,
    199
   ],
   [
    2,
    42,
    63,
    91,
    110,
    183,
    187,
    196
   ],
   [
    7,
    47,
    64,
    92,
    115,
    184,
    188,
    201
   ],
   [
    4,
    44,
    65,
    93,
    112,
    185,
    189,
    202
   ],
   [
    5,
    45,
    66,
    94,
    113,
    186,
    190,
    203
   ],
   [
    6,
    46,
    67,
    95,
    114,
    187,
    191,
    200
   ],
   [
    11,
    51,
    68,
    96,
    119,
    188,
    192,
    205
   ],
   [
    8,
    48,
    69,
    97,
    116,
    189,
    193,
    206
   ],
   [
    9,
    49,
    70,
    98,
    117,
    190,
    194,
    207
   ],
   [
    10,
    50,
    71,
    99,
    118,
    191,
    195,
    204
   ]
  ],
  "Z": [
   [
    11,
    20,
    24,
    97,
    116,
    144,
    165,
    205
   ],
   [
    8,
    21,
    25,
    98,
    117,
    145,
    166,
    206
   ],
   [
    9,
    22,
    26,
    99,
    118,
    146,
    167,
    207
   ],
   [
    10,
    23,
    27,
    96,
    119,
    147,
    164,
    204
   ],
   [
    15,
    24,
    28,
    101,
    120,
    148,
    169,
    209
   ],
   [
    12,
    25,
    29,
    102,
    121,
    149,
    170,
    210
   ],
   [
    13,
    26,
    30,
    103,
    122,
    150,
    171,
    211
   ],
   [
    14,
    27,
    31,
    100,
    123,
    151,
    168,
    208
   ],
   [
    19,
    28,
    32,
    105,
    124,
    152,
    173,
    213
   ],
   [
    16,
    29,
    33,
    106,
    125,
    153,
    174,
    214
   ],
   [
    17,
    30,
    34,
    107,
    126,
    154,
    175,
    215
   ],
   [
    18,
    31,
    35,
    104,
    127,
    155,
    172,
    212
   ],
   [
    1,
    23,
    32,
    36,
    109,
    128,
    156,
    177
   ],
   [
    2,
    20,
    33,
    37,
    110,
    129,
    157,
    178
   ],
   [
    3,
    21,
    34,
    38,
    111,
    130,
    158,
    179
   ],
   [
    0,
    22,
    35,
    39,
    108,
    131,
    159,
    176
   ],
   [
    5,
    27,
    36,
    40,
    113,
    132,
    160,
    181
   ],
   [
    6,
    24,
    37,
    41,
    114,
    133,
    161,
    182
   ],
   [
    7,
    25,
    38,
    42,
    115,
    134,
    162,
    183
   ],
   [
    4,
    26,
    39,
    43,
    112,
    135,
    163,
    180
   ],
   [
    9,
    31,
    40,
    44,
    117,
    136,
    164,
    185
   ],
   [
    10,
    28,
    41,
    45,
    118,
    137,
    165,
    186
   ],
   [
    11,
    29,
    42,
    46,
    119,
    138,
    166,
    187
   ],
   [
    8,
    30,
    43,
    47,
    116,
    139,
    167,
    184
   ],
   [
    13,
    35,
    44,
    48,
    121,
    140,
    168,
    189
   ],
   [
    14,
    32,
    45,
    49,
    122,
    141,
    169,
    190
   ],
   [
    15,
    33,
    46,
    50,
    123,
    142,
    170,
    191
   ],
   [
    12,
    34,
    47,
    51,
    120,
    143,
    171,
    188
   ],
   [
    17,
    39,
    48,
    52,
    125,
    144,
    172,
    193
   ],
   [
    18,
    36,
    49,
    53,
    126,
    145,
    173,
    194
   ],
   [
    19,
    37,
    50,
    54,
    127,
    146,
    174,
    195
   ],
   [
    16,
    38,
    51,
    55,
    124,
    147,
    175,
    192
   ],
   [
    21,
    43,
    52,
    56,
    129,
    148,
    176,
    197
   ],
   [
    22,
    40,
    53,
    57,
    130,
    149,
    177,
    198
   ],
   [
    23,
    41,
    54,
    58,
    131,
    150,
    178,
    199
   ],
   [
    20,
    42,
    55,
    59,
    128,
    151,
    179,
    196
   ],
   [
    25,
    47,
    56,
    60,
    133,
    152,
    180,
    201
   ],
   [
    26,
    44,
    57,
    61,
    134,
    153,
    181,
    202
   ],
   [
    27,
    45,
    58,
    62,
    135,
    154,
    182,
    203
   ],
   [
    24,
    46,
    59,
    63,
    132,
    155,
    183,
    200
   ],
   [
    29,
    51,
    60,
    64,
    137,
    156,
    184,
    205
   ],
   [
    30,
    48,
    61,
    65,
    138,
    157,
    185,
    206
   ],
   [
    31,
    49,
    62,
    66,
    139,
    158,
    186,
    207
   ],
   [
    28,
    50,
    63,
    67,
    136,
    159,
    187,
    204
   ],
   [
    33,
    55,
    64,
    68,
    141,
    160,
    188,
    209
   ],
   [
    34,
    52,
    65,
    69,
    142,
    161,
    189,
    210
   ],
   [
    35,
    53,
    66,
    70,
    143,
    162,
    190,
    211
   ],
   [
    32,
    54,
    67,
    71,
    140,
    163,
    191,
    208
   ],
   [
    37,
    59,
    68,
    72,
    145,
    164,
    192,
    213
   ],
   [
    38,
    56,
    69,
    73,
    146,
    165,
    193,
    214
   ],
   [
    39,
    57,
    70,
    74,
    147,
    166,
    194,
    215
   ],
   [
    36,
    58,
    71,
    75,
    144,
    167,
    195,
    212
   ],
   [
    41,
    63,
    72,
    76,
    109,
    149,
    168,
    196
   ],
   [
    42,
    60,
    73,
    77,
    110,
    150,
    169,
    197
   ],
   [
    43,
    61,
    74,
    78,
    111,
    151,
    170,
    198
   ],
   [
    40,
    62,
    75,
    79,
    108,
    148,
    171,
    199
   ],
   [
    45,
    67,
    76,
    80,
    113,
    153,
    172,
    200
   ],
   [
    46,
    64,
    77,
    81,
    114,
    154,
    173,
    201
   ],
   [
    47,
    65,
    78,
    82,
    115,
    155,
    174,
    202
   ],
   [
    44,
    66,
    79,
    83,
    112,
    152,
    175,
    203
   ],
   [
    49,
    71,
    80,
    84,
    117,
    157,
    176,
    204
   ],
   [
    50,
    68,
    81,
    85,
    118,
    158,
    177,
    205
   ],
   [
    51,
    69,
    82,
    86,
    119,
    159,
    178,
    206
   ],
   [
    48,
    70,
    83,
    87,
    116,
    156,
    179,
    207
   ],
   [
    53,
    75,
    84,
    88,
    121,
    161,
    180,
    208
   ],
   [
    54,
    72,
    85,
    89,
    122,
    162,
    181,
    209
   ],
   [
    55,
    73,
    86,
    90,
    123,
    163,
    182,
    210
   ],
   [
    52,
    74,
    87,
    91,
    120,
    160,
    183,
    211
   ],
   [
    57,
    79,
    88,
    92,
    125,
    165,
    184,
    212
   ],
   [
    58,
    76,
    89,
    93,
    126,
    166,
    185,
    213
   ],
   [
    59,
    77,
    90,
    94,
    127,
    167,
    186,
    214
   ],
   [
    56,
    78,
    91,
    95,
    124,
    164,
    187,
    215
   ],
   [
    61,
    83,
    92,
    96,
    108,
    129,
    169,
    188
   ],
   [
    62,
    80,
    93,
    97,
    109,
    130,
    170,
    189
   ],
   [
    63,
    81,
    94,
    98,
    110,
    131,
    171,
    190
   ],
   [
    60,
    82,
    95,
    99,
    111,
    128,
    168,
    191
   ],
   [
    65,
    87,
    96,
    100,
    112,
    133,
    173,
    192
   ],
   [
    66,
    84,
    97,
    101,
    113,
    134,
    174,
    193
   ],
   [
    67,
    85,
    98,
    102,
    114,
    135,
    175,
    194
   ],
   [
    64,
    86,
    99,
    103,
    115,
    132,
    172,
    195
   ],
   [
    69,
    91,
    100,
    104,
    116,
    137,
    177,
    196
   ],
   [
    70,
    88,
    101,
    105,
    117,
    138,
    178,
    197
   ],
   [
    71,
    89,
    102,
    106,
    118,
    139,
    179,
    198
   ],
   [
    68,
    90,
    103,
    107,
    119,
    136,
    176,
    199
   ],
   [
    0,
    73,
    95,
    104,
    120,
    141,
    181,
    200
   ],
   [
    1,
    74,
    92,
    105,
    121,
    142,
    182,
    201
   ],
   [
    2,
    75,
    93,
    106,
    122,
    143,
    183,
    202
   ],
   [
    3,
    72,
    94,
    107,
    123,
    140,
    180,
    203
   ],
   [
    0,
    4,
    77,
    99,
    124,
    145,
    185,
    204
   ],
   [
    1,
    5,
    78,
    96,
    125,
    146,
    186,
    205
   ],
   [
    2,
    6,
    79,
    97,
    126,
    147,
    187,
    206
   ],
   [
    3,
    7,
    76,
    98,
    127,
    144,
    184,
    207
   ],
   [
    4,
    8,
    81,
    103,
    128,
    149,
    189,
    208
   ],
   [
    5,
    9,
    82,
    100,
    129,
    150,
    190,
    209
   ],
   [
    6,
    10,
    83,
    101,
    130,
    151,
    191,
    210
   ],
   [
    7,
    11,
    80,
    102,
    131,
    148,
    188,
    211
   ],
   [
    8,
    12,
    85,
    107,
    132,
    153,
    193,
    212
   ],
   [
    9,
    13,
    86,
    104,
    133,
    154,
    194,
    213
   ],
   [
    10,
    14,
    87,
    105,
    134,
    155,
    195,
    214
   ],
   [
    11,
    15,
    84,
    106,
    135,
    152,
    192,
    215
   ],
   [
    3,
    12,
    16,
    89,
    108,
    136,
    157,
    197
   ],
   [
    0,
    13,
    17,
    90,
    109,
    137,
    158,
    198
   ],
   [
    1,
    14,
    18,
    91,
    110,
    138,
    159,
    199
   ],
   [
    2,
    15,
    19,
    88,
    111,
    139,
    156,
    196
   ],
   [
    7,
    16,
    20,
    93,
    112,
    140,
    161,
    201
   ],
   [
    4,
    17,
    21,
    94,
    113,
    141,
    162,
    202
   ],
   [
    5,
    18,
    22,
    95,
    114,
    142,
    163,
    203
   ],
   [
    6,
    19,
    23,
    92,
    115,
    143,
    160,
    200
   ]
  ]
 },
 "distance": {
  "d": 21,
  "X": {
   "value": 21,
   "confidence": "upper_bound",
   "witness": [
    3,
    6,
    16,
    19,
    30,
    41,
    44,
    45,
    54,
    57,
    62,
    76,
    79,
    106,
    122,
    124,
    130,
    139,
    140,
    185,
    215
   ]
  },
  "Z": {
   "value": 21,
   "confidence": "upper_bound",
   "witness": [
    8,
    53,
    58,
    67,
    69,
    75,
    90,
    117,
    118,
    135,
    136,
    143,
    148,
    149,
    152,
    167,
    177,
    178,
    191,
    194,
    199
   ]
  }
 },
 "provenance": {
  "authors": [
   "@MathysRennela"
  ],
  "construction": "Bivariate bicycle code QC(A,B) on Z_27 x Z_4 with weight-4 generators A = x^3 y^3 + x^13 y^3 + x^18 + x^25, B = x^3 y^3 + x^21 + x^22 + x^25 y (weight-8 checks). Found by campaign 2 of a weight-8 BB sweep at n in {192, 216, 288}, beyond the regime searched by arXiv:2609.06572.",
  "origin": "submission",
  "date": "2026-09-09",
  "model": "Omen Alpha 1.0",
  "notes": "New parameters (submitter claim). Distance: RIS upper bound d<=21 (20k trials), corroborated by BP+OSD at 200k trials/side finding nothing lighter; exact certification not run.",
  "novelty": "new_parameters"
 },
 "family": "bivariate-bicycle"
}
