{
 "schema_version": "0.1",
 "name": "[[234,26,7]] periodic bivariate-bicycle on Z_9 x Z_13",
 "code_type": "CSS",
 "n": 234,
 "k": 26,
 "checks": {
  "X": [
   [
    0,
    7,
    33,
    65,
    117,
    130
   ],
   [
    1,
    8,
    34,
    66,
    118,
    131
   ],
   [
    2,
    9,
    35,
    67,
    119,
    132
   ],
   [
    3,
    10,
    36,
    68,
    120,
    133
   ],
   [
    4,
    11,
    37,
    69,
    121,
    134
   ],
   [
    5,
    12,
    38,
    70,
    122,
    135
   ],
   [
    0,
    6,
    26,
    71,
    123,
    136
   ],
   [
    1,
    7,
    27,
    72,
    124,
    137
   ],
   [
    2,
    8,
    28,
    73,
    125,
    138
   ],
   [
    3,
    9,
    29,
    74,
    126,
    139
   ],
   [
    4,
    10,
    30,
    75,
    127,
    140
   ],
   [
    5,
    11,
    31,
    76,
    128,
    141
   ],
   [
    6,
    12,
    32,
    77,
    129,
    142
   ],
   [
    13,
    20,
    46,
    78,
    130,
    143
   ],
   [
    14,
    21,
    47,
    79,
    131,
    144
   ],
   [
    15,
    22,
    48,
    80,
    132,
    145
   ],
   [
    16,
    23,
    49,
    81,
    133,
    146
   ],
   [
    17,
    24,
    50,
    82,
    134,
    147
   ],
   [
    18,
    25,
    51,
    83,
    135,
    148
   ],
   [
    13,
    19,
    39,
    84,
    136,
    149
   ],
   [
    14,
    20,
    40,
    85,
    137,
    150
   ],
   [
    15,
    21,
    41,
    86,
    138,
    151
   ],
   [
    16,
    22,
    42,
    87,
    139,
    152
   ],
   [
    17,
    23,
    43,
    88,
    140,
    153
   ],
   [
    18,
    24,
    44,
    89,
    141,
    154
   ],
   [
    19,
    25,
    45,
    90,
    142,
    155
   ],
   [
    26,
    33,
    59,
    91,
    143,
    156
   ],
   [
    27,
    34,
    60,
    92,
    144,
    157
   ],
   [
    28,
    35,
    61,
    93,
    145,
    158
   ],
   [
    29,
    36,
    62,
    94,
    146,
    159
   ],
   [
    30,
    37,
    63,
    95,
    147,
    160
   ],
   [
    31,
    38,
    64,
    96,
    148,
    161
   ],
   [
    26,
    32,
    52,
    97,
    149,
    162
   ],
   [
    27,
    33,
    53,
    98,
    150,
    163
   ],
   [
    28,
    34,
    54,
    99,
    151,
    164
   ],
   [
    29,
    35,
    55,
    100,
    152,
    165
   ],
   [
    30,
    36,
    56,
    101,
    153,
    166
   ],
   [
    31,
    37,
    57,
    102,
    154,
    167
   ],
   [
    32,
    38,
    58,
    103,
    155,
    168
   ],
   [
    39,
    46,
    72,
    104,
    156,
    169
   ],
   [
    40,
    47,
    73,
    105,
    157,
    170
   ],
   [
    41,
    48,
    74,
    106,
    158,
    171
   ],
   [
    42,
    49,
    75,
    107,
    159,
    172
   ],
   [
    43,
    50,
    76,
    108,
    160,
    173
   ],
   [
    44,
    51,
    77,
    109,
    161,
    174
   ],
   [
    39,
    45,
    65,
    110,
    162,
    175
   ],
   [
    40,
    46,
    66,
    111,
    163,
    176
   ],
   [
    41,
    47,
    67,
    112,
    164,
    177
   ],
   [
    42,
    48,
    68,
    113,
    165,
    178
   ],
   [
    43,
    49,
    69,
    114,
    166,
    179
   ],
   [
    44,
    50,
    70,
    115,
    167,
    180
   ],
   [
    45,
    51,
    71,
    116,
    168,
    181
   ],
   [
    0,
    52,
    59,
    85,
    169,
    182
   ],
   [
    1,
    53,
    60,
    86,
    170,
    183
   ],
   [
    2,
    54,
    61,
    87,
    171,
    184
   ],
   [
    3,
    55,
    62,
    88,
    172,
    185
   ],
   [
    4,
    56,
    63,
    89,
    173,
    186
   ],
   [
    5,
    57,
    64,
    90,
    174,
    187
   ],
   [
    6,
    52,
    58,
    78,
    175,
    188
   ],
   [
    7,
    53,
    59,
    79,
    176,
    189
   ],
   [
    8,
    54,
    60,
    80,
    177,
    190
   ],
   [
    9,
    55,
    61,
    81,
    178,
    191
   ],
   [
    10,
    56,
    62,
    82,
    179,
    192
   ],
   [
    11,
    57,
    63,
    83,
    180,
    193
   ],
   [
    12,
    58,
    64,
    84,
    181,
    194
   ],
   [
    13,
    65,
    72,
    98,
    182,
    195
   ],
   [
    14,
    66,
    73,
    99,
    183,
    196
   ],
   [
    15,
    67,
    74,
    100,
    184,
    197
   ],
   [
    16,
    68,
    75,
    101,
    185,
    198
   ],
   [
    17,
    69,
    76,
    102,
    186,
    199
   ],
   [
    18,
    70,
    77,
    103,
    187,
    200
   ],
   [
    19,
    65,
    71,
    91,
    188,
    201
   ],
   [
    20,
    66,
    72,
    92,
    189,
    202
   ],
   [
    21,
    67,
    73,
    93,
    190,
    203
   ],
   [
    22,
    68,
    74,
    94,
    191,
    204
   ],
   [
    23,
    69,
    75,
    95,
    192,
    205
   ],
   [
    24,
    70,
    76,
    96,
    193,
    206
   ],
   [
    25,
    71,
    77,
    97,
    194,
    207
   ],
   [
    26,
    78,
    85,
    111,
    195,
    208
   ],
   [
    27,
    79,
    86,
    112,
    196,
    209
   ],
   [
    28,
    80,
    87,
    113,
    197,
    210
   ],
   [
    29,
    81,
    88,
    114,
    198,
    211
   ],
   [
    30,
    82,
    89,
    115,
    199,
    212
   ],
   [
    31,
    83,
    90,
    116,
    200,
    213
   ],
   [
    32,
    78,
    84,
    104,
    201,
    214
   ],
   [
    33,
    79,
    85,
    105,
    202,
    215
   ],
   [
    34,
    80,
    86,
    106,
    203,
    216
   ],
   [
    35,
    81,
    87,
    107,
    204,
    217
   ],
   [
    36,
    82,
    88,
    108,
    205,
    218
   ],
   [
    37,
    83,
    89,
    109,
    206,
    219
   ],
   [
    38,
    84,
    90,
    110,
    207,
    220
   ],
   [
    7,
    39,
    91,
    98,
    208,
    221
   ],
   [
    8,
    40,
    92,
    99,
    209,
    222
   ],
   [
    9,
    41,
    93,
    100,
    210,
    223
   ],
   [
    10,
    42,
    94,
    101,
    211,
    224
   ],
   [
    11,
    43,
    95,
    102,
    212,
    225
   ],
   [
    12,
    44,
    96,
    103,
    213,
    226
   ],
   [
    0,
    45,
    91,
    97,
    214,
    227
   ],
   [
    1,
    46,
    92,
    98,
    215,
    228
   ],
   [
    2,
    47,
    93,
    99,
    216,
    229
   ],
   [
    3,
    48,
    94,
    100,
    217,
    230
   ],
   [
    4,
    49,
    95,
    101,
    218,
    231
   ],
   [
    5,
    50,
    96,
    102,
    219,
    232
   ],
   [
    6,
    51,
    97,
    103,
    220,
    233
   ],
   [
    20,
    52,
    104,
    111,
    117,
    221
   ],
   [
    21,
    53,
    105,
    112,
    118,
    222
   ],
   [
    22,
    54,
    106,
    113,
    119,
    223
   ],
   [
    23,
    55,
    107,
    114,
    120,
    224
   ],
   [
    24,
    56,
    108,
    115,
    121,
    225
   ],
   [
    25,
    57,
    109,
    116,
    122,
    226
   ],
   [
    13,
    58,
    104,
    110,
    123,
    227
   ],
   [
    14,
    59,
    105,
    111,
    124,
    228
   ],
   [
    15,
    60,
    106,
    112,
    125,
    229
   ],
   [
    16,
    61,
    107,
    113,
    126,
    230
   ],
   [
    17,
    62,
    108,
    114,
    127,
    231
   ],
   [
    18,
    63,
    109,
    115,
    128,
    232
   ],
   [
    19,
    64,
    110,
    116,
    129,
    233
   ]
  ],
  "Z": [
   [
    0,
    104,
    117,
    123,
    169,
    214
   ],
   [
    1,
    105,
    118,
    124,
    170,
    215
   ],
   [
    2,
    106,
    119,
    125,
    171,
    216
   ],
   [
    3,
    107,
    120,
    126,
    172,
    217
   ],
   [
    4,
    108,
    121,
    127,
    173,
    218
   ],
   [
    5,
    109,
    122,
    128,
    174,
    219
   ],
   [
    6,
    110,
    123,
    129,
    175,
    220
   ],
   [
    7,
    111,
    117,
    124,
    176,
    208
   ],
   [
    8,
    112,
    118,
    125,
    177,
    209
   ],
   [
    9,
    113,
    119,
    126,
    178,
    210
   ],
   [
    10,
    114,
    120,
    127,
    179,
    211
   ],
   [
    11,
    115,
    121,
    128,
    180,
    212
   ],
   [
    12,
    116,
    122,
    129,
    181,
    213
   ],
   [
    0,
    13,
    130,
    136,
    182,
    227
   ],
   [
    1,
    14,
    131,
    137,
    183,
    228
   ],
   [
    2,
    15,
    132,
    138,
    184,
    229
   ],
   [
    3,
    16,
    133,
    139,
    185,
    230
   ],
   [
    4,
    17,
    134,
    140,
    186,
    231
   ],
   [
    5,
    18,
    135,
    141,
    187,
    232
   ],
   [
    6,
    19,
    136,
    142,
    188,
    233
   ],
   [
    7,
    20,
    130,
    137,
    189,
    221
   ],
   [
    8,
    21,
    131,
    138,
    190,
    222
   ],
   [
    9,
    22,
    132,
    139,
    191,
    223
   ],
   [
    10,
    23,
    133,
    140,
    192,
    224
   ],
   [
    11,
    24,
    134,
    141,
    193,
    225
   ],
   [
    12,
    25,
    135,
    142,
    194,
    226
   ],
   [
    13,
    26,
    123,
    143,
    149,
    195
   ],
   [
    14,
    27,
    124,
    144,
    150,
    196
   ],
   [
    15,
    28,
    125,
    145,
    151,
    197
   ],
   [
    16,
    29,
    126,
    146,
    152,
    198
   ],
   [
    17,
    30,
    127,
    147,
    153,
    199
   ],
   [
    18,
    31,
    128,
    148,
    154,
    200
   ],
   [
    19,
    32,
    129,
    149,
    155,
    201
   ],
   [
    20,
    33,
    117,
    143,
    150,
    202
   ],
   [
    21,
    34,
    118,
    144,
    151,
    203
   ],
   [
    22,
    35,
    119,
    145,
    152,
    204
   ],
   [
    23,
    36,
    120,
    146,
    153,
    205
   ],
   [
    24,
    37,
    121,
    147,
    154,
    206
   ],
   [
    25,
    38,
    122,
    148,
    155,
    207
   ],
   [
    26,
    39,
    136,
    156,
    162,
    208
   ],
   [
    27,
    40,
    137,
    157,
    163,
    209
   ],
   [
    28,
    41,
    138,
    158,
    164,
    210
   ],
   [
    29,
    42,
    139,
    159,
    165,
    211
   ],
   [
    30,
    43,
    140,
    160,
    166,
    212
   ],
   [
    31,
    44,
    141,
    161,
    167,
    213
   ],
   [
    32,
    45,
    142,
    162,
    168,
    214
   ],
   [
    33,
    46,
    130,
    156,
    163,
    215
   ],
   [
    34,
    47,
    131,
    157,
    164,
    216
   ],
   [
    35,
    48,
    132,
    158,
    165,
    217
   ],
   [
    36,
    49,
    133,
    159,
    166,
    218
   ],
   [
    37,
    50,
    134,
    160,
    167,
    219
   ],
   [
    38,
    51,
    135,
    161,
    168,
    220
   ],
   [
    39,
    52,
    149,
    169,
    175,
    221
   ],
   [
    40,
    53,
    150,
    170,
    176,
    222
   ],
   [
    41,
    54,
    151,
    171,
    177,
    223
   ],
   [
    42,
    55,
    152,
    172,
    178,
    224
   ],
   [
    43,
    56,
    153,
    173,
    179,
    225
   ],
   [
    44,
    57,
    154,
    174,
    180,
    226
   ],
   [
    45,
    58,
    155,
    175,
    181,
    227
   ],
   [
    46,
    59,
    143,
    169,
    176,
    228
   ],
   [
    47,
    60,
    144,
    170,
    177,
    229
   ],
   [
    48,
    61,
    145,
    171,
    178,
    230
   ],
   [
    49,
    62,
    146,
    172,
    179,
    231
   ],
   [
    50,
    63,
    147,
    173,
    180,
    232
   ],
   [
    51,
    64,
    148,
    174,
    181,
    233
   ],
   [
    52,
    65,
    117,
    162,
    182,
    188
   ],
   [
    53,
    66,
    118,
    163,
    183,
    189
   ],
   [
    54,
    67,
    119,
    164,
    184,
    190
   ],
   [
    55,
    68,
    120,
    165,
    185,
    191
   ],
   [
    56,
    69,
    121,
    166,
    186,
    192
   ],
   [
    57,
    70,
    122,
    167,
    187,
    193
   ],
   [
    58,
    71,
    123,
    168,
    188,
    194
   ],
   [
    59,
    72,
    124,
    156,
    182,
    189
   ],
   [
    60,
    73,
    125,
    157,
    183,
    190
   ],
   [
    61,
    74,
    126,
    158,
    184,
    191
   ],
   [
    62,
    75,
    127,
    159,
    185,
    192
   ],
   [
    63,
    76,
    128,
    160,
    186,
    193
   ],
   [
    64,
    77,
    129,
    161,
    187,
    194
   ],
   [
    65,
    78,
    130,
    175,
    195,
    201
   ],
   [
    66,
    79,
    131,
    176,
    196,
    202
   ],
   [
    67,
    80,
    132,
    177,
    197,
    203
   ],
   [
    68,
    81,
    133,
    178,
    198,
    204
   ],
   [
    69,
    82,
    134,
    179,
    199,
    205
   ],
   [
    70,
    83,
    135,
    180,
    200,
    206
   ],
   [
    71,
    84,
    136,
    181,
    201,
    207
   ],
   [
    72,
    85,
    137,
    169,
    195,
    202
   ],
   [
    73,
    86,
    138,
    170,
    196,
    203
   ],
   [
    74,
    87,
    139,
    171,
    197,
    204
   ],
   [
    75,
    88,
    140,
    172,
    198,
    205
   ],
   [
    76,
    89,
    141,
    173,
    199,
    206
   ],
   [
    77,
    90,
    142,
    174,
    200,
    207
   ],
   [
    78,
    91,
    143,
    188,
    208,
    214
   ],
   [
    79,
    92,
    144,
    189,
    209,
    215
   ],
   [
    80,
    93,
    145,
    190,
    210,
    216
   ],
   [
    81,
    94,
    146,
    191,
    211,
    217
   ],
   [
    82,
    95,
    147,
    192,
    212,
    218
   ],
   [
    83,
    96,
    148,
    193,
    213,
    219
   ],
   [
    84,
    97,
    149,
    194,
    214,
    220
   ],
   [
    85,
    98,
    150,
    182,
    208,
    215
   ],
   [
    86,
    99,
    151,
    183,
    209,
    216
   ],
   [
    87,
    100,
    152,
    184,
    210,
    217
   ],
   [
    88,
    101,
    153,
    185,
    211,
    218
   ],
   [
    89,
    102,
    154,
    186,
    212,
    219
   ],
   [
    90,
    103,
    155,
    187,
    213,
    220
   ],
   [
    91,
    104,
    156,
    201,
    221,
    227
   ],
   [
    92,
    105,
    157,
    202,
    222,
    228
   ],
   [
    93,
    106,
    158,
    203,
    223,
    229
   ],
   [
    94,
    107,
    159,
    204,
    224,
    230
   ],
   [
    95,
    108,
    160,
    205,
    225,
    231
   ],
   [
    96,
    109,
    161,
    206,
    226,
    232
   ],
   [
    97,
    110,
    162,
    207,
    227,
    233
   ],
   [
    98,
    111,
    163,
    195,
    221,
    228
   ],
   [
    99,
    112,
    164,
    196,
    222,
    229
   ],
   [
    100,
    113,
    165,
    197,
    223,
    230
   ],
   [
    101,
    114,
    166,
    198,
    224,
    231
   ],
   [
    102,
    115,
    167,
    199,
    225,
    232
   ],
   [
    103,
    116,
    168,
    200,
    226,
    233
   ]
  ]
 },
 "distance": {
  "d": 7,
  "X": {
   "value": 7,
   "confidence": "exact",
   "witness": [
    9,
    22,
    35,
    48,
    55,
    68,
    178
   ]
  },
  "Z": {
   "value": 7,
   "confidence": "exact",
   "witness": [
    0,
    39,
    65,
    91,
    136,
    156,
    182
   ]
  }
 },
 "family": "bivariate-bicycle",
 "provenance": {
  "authors": [
   "@cbjuan"
  ],
  "construction": "Periodic bivariate-bicycle code on the group algebra Z_9 x Z_13 (n = 2*l*m = 234). Convention: x = S_9 tensor I_13, y = I_9 tensor S_13 (cyclic shifts), qubit index = i*m + j; A = 1 + x^0y^7 + x^2y^7 + x^5y^0, B = 1 + x^1y^0; H_X = [A|B], H_Z = [B^T|A^T]. Found by an automated evolutionary/mutation search over (l, m, A, B) exponent sets targeting the unrestricted x weight-6 (or weight-8) board cells, screened by a randomized lightest-logical surrogate and promoted through increasing trial budgets.",
  "origin": "submission",
  "date": "2026-09-16",
  "notes": "Internal autoresearch candidate id 20918 (canonical key 56134fef1933d3ee59cc338a), search lane 'targeted-mutation', proposal kernel 'nearby-geometry'. Initial NumPy lightest-logical surrogate: trials=8000, seed=1591394722. Confirmed with an accelerated bit-packed random-information-set search at rung '60k' (60000 trials, seed=1591394739, pair_depth=16), tightest witness on side X at weight 7. Distance also taken through an internal exact-certification pipeline (MILP, one solve per logical-basis row per side, the same method as this repository's own verify/certify.py). Result: side_status X=exact, Z=exact (solver wall time 25452.4s, CPU time 25184.2s, summed over all per-row MILP solves on both sides). Per CONTRIBUTING.md's confidence-tier policy, this 'exact' claim is self-declared and will display as an upper bound on the board until a maintainer independently re-runs verify/certify.py and confirms it."
 }
}
