{
 "schema_version": "0.2",
 "name": "[[204,28,12]] two-block code over C102",
 "code_type": "CSS",
 "n": 204,
 "k": 28,
 "checks": {
  "X": [
   [
    0,
    8,
    45,
    87,
    102,
    114,
    146,
    150
   ],
   [
    1,
    11,
    42,
    84,
    103,
    117,
    149,
    153
   ],
   [
    2,
    13,
    35,
    77,
    104,
    105,
    140,
    151
   ],
   [
    3,
    14,
    51,
    93,
    105,
    120,
    152,
    156
   ],
   [
    4,
    16,
    32,
    74,
    106,
    107,
    143,
    154
   ],
   [
    5,
    17,
    48,
    90,
    107,
    123,
    155,
    159
   ],
   [
    6,
    18,
    40,
    82,
    108,
    109,
    145,
    156
   ],
   [
    7,
    19,
    41,
    83,
    109,
    110,
    146,
    157
   ],
   [
    8,
    20,
    57,
    98,
    110,
    126,
    158,
    162
   ],
   [
    9,
    21,
    37,
    79,
    111,
    112,
    148,
    159
   ],
   [
    10,
    22,
    38,
    80,
    112,
    113,
    149,
    160
   ],
   [
    11,
    23,
    54,
    96,
    113,
    129,
    161,
    165
   ],
   [
    12,
    24,
    46,
    88,
    114,
    115,
    151,
    162
   ],
   [
    13,
    25,
    47,
    89,
    115,
    116,
    152,
    163
   ],
   [
    14,
    26,
    63,
    101,
    116,
    132,
    164,
    168
   ],
   [
    15,
    27,
    43,
    85,
    117,
    118,
    154,
    165
   ],
   [
    16,
    28,
    44,
    86,
    118,
    119,
    155,
    166
   ],
   [
    17,
    29,
    60,
    100,
    119,
    135,
    167,
    171
   ],
   [
    18,
    30,
    52,
    94,
    120,
    121,
    157,
    168
   ],
   [
    19,
    31,
    53,
    95,
    121,
    122,
    158,
    169
   ],
   [
    9,
    20,
    32,
    69,
    122,
    138,
    170,
    174
   ],
   [
    21,
    33,
    49,
    91,
    123,
    124,
    160,
    171
   ],
   [
    22,
    34,
    50,
    92,
    124,
    125,
    161,
    172
   ],
   [
    6,
    23,
    35,
    66,
    125,
    141,
    173,
    177
   ],
   [
    24,
    36,
    58,
    99,
    126,
    127,
    163,
    174
   ],
   [
    1,
    25,
    37,
    59,
    127,
    128,
    164,
    175
   ],
   [
    15,
    26,
    38,
    75,
    128,
    144,
    176,
    180
   ],
   [
    27,
    39,
    55,
    97,
    129,
    130,
    166,
    177
   ],
   [
    0,
    28,
    40,
    56,
    130,
    131,
    167,
    178
   ],
   [
    12,
    29,
    41,
    72,
    131,
    147,
    179,
    183
   ],
   [
    4,
    30,
    42,
    64,
    132,
    133,
    169,
    180
   ],
   [
    5,
    31,
    43,
    65,
    133,
    134,
    170,
    181
   ],
   [
    21,
    32,
    44,
    81,
    134,
    150,
    182,
    186
   ],
   [
    2,
    33,
    45,
    61,
    135,
    136,
    172,
    183
   ],
   [
    3,
    34,
    46,
    62,
    136,
    137,
    173,
    184
   ],
   [
    18,
    35,
    47,
    78,
    137,
    153,
    185,
    189
   ],
   [
    10,
    36,
    48,
    70,
    138,
    139,
    175,
    186
   ],
   [
    11,
    37,
    49,
    71,
    139,
    140,
    176,
    187
   ],
   [
    27,
    38,
    50,
    87,
    140,
    156,
    188,
    192
   ],
   [
    7,
    39,
    51,
    67,
    141,
    142,
    178,
    189
   ],
   [
    8,
    40,
    52,
    68,
    142,
    143,
    179,
    190
   ],
   [
    24,
    41,
    53,
    84,
    143,
    159,
    191,
    195
   ],
   [
    16,
    42,
    54,
    76,
    144,
    145,
    181,
    192
   ],
   [
    17,
    43,
    55,
    77,
    145,
    146,
    182,
    193
   ],
   [
    33,
    44,
    56,
    93,
    146,
    162,
    194,
    198
   ],
   [
    13,
    45,
    57,
    73,
    147,
    148,
    184,
    195
   ],
   [
    14,
    46,
    58,
    74,
    148,
    149,
    185,
    196
   ],
   [
    30,
    47,
    59,
    90,
    149,
    165,
    197,
    200
   ],
   [
    22,
    48,
    60,
    82,
    150,
    151,
    187,
    198
   ],
   [
    23,
    49,
    61,
    83,
    151,
    152,
    188,
    199
   ],
   [
    39,
    50,
    62,
    98,
    102,
    152,
    168,
    202
   ],
   [
    19,
    51,
    63,
    79,
    153,
    154,
    190,
    200
   ],
   [
    20,
    52,
    64,
    80,
    154,
    155,
    191,
    201
   ],
   [
    36,
    53,
    65,
    96,
    103,
    155,
    171,
    203
   ],
   [
    28,
    54,
    66,
    88,
    156,
    157,
    193,
    202
   ],
   [
    29,
    55,
    67,
    89,
    104,
    157,
    158,
    194
   ],
   [
    45,
    56,
    68,
    101,
    105,
    108,
    158,
    174
   ],
   [
    25,
    57,
    69,
    85,
    159,
    160,
    196,
    203
   ],
   [
    26,
    58,
    70,
    86,
    106,
    160,
    161,
    197
   ],
   [
    42,
    59,
    71,
    100,
    107,
    111,
    161,
    177
   ],
   [
    34,
    60,
    72,
    94,
    108,
    162,
    163,
    199
   ],
   [
    35,
    61,
    73,
    95,
    102,
    109,
    163,
    164
   ],
   [
    9,
    51,
    62,
    74,
    110,
    114,
    164,
    180
   ],
   [
    31,
    63,
    75,
    91,
    111,
    165,
    166,
    201
   ],
   [
    32,
    64,
    76,
    92,
    103,
    112,
    166,
    167
   ],
   [
    6,
    48,
    65,
    77,
    113,
    117,
    167,
    183
   ],
   [
    40,
    66,
    78,
    99,
    104,
    114,
    168,
    169
   ],
   [
    1,
    41,
    67,
    79,
    105,
    115,
    169,
    170
   ],
   [
    15,
    57,
    68,
    80,
    116,
    120,
    170,
    186
   ],
   [
    37,
    69,
    81,
    97,
    106,
    117,
    171,
    172
   ],
   [
    0,
    38,
    70,
    82,
    107,
    118,
    172,
    173
   ],
   [
    12,
    54,
    71,
    83,
    119,
    123,
    173,
    189
   ],
   [
    4,
    46,
    72,
    84,
    109,
    120,
    174,
    175
   ],
   [
    5,
    47,
    73,
    85,
    110,
    121,
    175,
    176
   ],
   [
    21,
    63,
    74,
    86,
    122,
    126,
    176,
    192
   ],
   [
    2,
    43,
    75,
    87,
    112,
    123,
    177,
    178
   ],
   [
    3,
    44,
    76,
    88,
    113,
    124,
    178,
    179
   ],
   [
    18,
    60,
    77,
    89,
    125,
    129,
    179,
    195
   ],
   [
    10,
    52,
    78,
    90,
    115,
    126,
    180,
    181
   ],
   [
    11,
    53,
    79,
    91,
    116,
    127,
    181,
    182
   ],
   [
    27,
    69,
    80,
    92,
    128,
    132,
    182,
    198
   ],
   [
    7,
    49,
    81,
    93,
    118,
    129,
    183,
    184
   ],
   [
    8,
    50,
    82,
    94,
    119,
    130,
    184,
    185
   ],
   [
    24,
    66,
    83,
    95,
    131,
    135,
    185,
    200
   ],
   [
    16,
    58,
    84,
    96,
    121,
    132,
    186,
    187
   ],
   [
    17,
    59,
    85,
    97,
    122,
    133,
    187,
    188
   ],
   [
    0,
    33,
    75,
    86,
    134,
    138,
    188,
    202
   ],
   [
    13,
    55,
    87,
    98,
    124,
    135,
    189,
    190
   ],
   [
    14,
    56,
    88,
    99,
    125,
    136,
    190,
    191
   ],
   [
    1,
    30,
    72,
    89,
    137,
    141,
    191,
    203
   ],
   [
    22,
    64,
    90,
    100,
    127,
    138,
    192,
    193
   ],
   [
    2,
    23,
    65,
    91,
    128,
    139,
    193,
    194
   ],
   [
    3,
    39,
    81,
    92,
    108,
    140,
    144,
    194
   ],
   [
    19,
    61,
    93,
    101,
    130,
    141,
    195,
    196
   ],
   [
    4,
    20,
    62,
    94,
    131,
    142,
    196,
    197
   ],
   [
    5,
    36,
    78,
    95,
    111,
    143,
    147,
    197
   ],
   [
    6,
    28,
    70,
    96,
    133,
    144,
    198,
    199
   ],
   [
    7,
    29,
    71,
    97,
    102,
    134,
    145,
    199
   ],
   [
    9,
    25,
    67,
    98,
    136,
    147,
    200,
    201
   ],
   [
    10,
    26,
    68,
    99,
    103,
    137,
    148,
    201
   ],
   [
    12,
    34,
    76,
    100,
    104,
    139,
    150,
    202
   ],
   [
    15,
    31,
    73,
    101,
    106,
    142,
    153,
    203
   ]
  ],
  "Z": [
   [
    0,
    50,
    61,
    97,
    102,
    130,
    172,
    188
   ],
   [
    1,
    53,
    64,
    99,
    103,
    127,
    169,
    191
   ],
   [
    2,
    55,
    66,
    100,
    104,
    135,
    177,
    193
   ],
   [
    2,
    3,
    56,
    67,
    105,
    136,
    178,
    194
   ],
   [
    4,
    58,
    69,
    101,
    106,
    132,
    174,
    196
   ],
   [
    4,
    5,
    59,
    70,
    107,
    133,
    175,
    197
   ],
   [
    6,
    56,
    60,
    92,
    108,
    125,
    167,
    198
   ],
   [
    6,
    7,
    61,
    72,
    109,
    141,
    183,
    199
   ],
   [
    7,
    8,
    62,
    73,
    102,
    110,
    142,
    184
   ],
   [
    9,
    59,
    63,
    95,
    111,
    122,
    164,
    200
   ],
   [
    9,
    10,
    64,
    75,
    112,
    138,
    180,
    201
   ],
   [
    10,
    11,
    65,
    76,
    103,
    113,
    139,
    181
   ],
   [
    0,
    12,
    62,
    66,
    114,
    131,
    173,
    202
   ],
   [
    12,
    13,
    67,
    78,
    104,
    115,
    147,
    189
   ],
   [
    13,
    14,
    68,
    79,
    105,
    116,
    148,
    190
   ],
   [
    1,
    15,
    65,
    69,
    117,
    128,
    170,
    203
   ],
   [
    15,
    16,
    70,
    81,
    106,
    118,
    144,
    186
   ],
   [
    16,
    17,
    71,
    82,
    107,
    119,
    145,
    187
   ],
   [
    3,
    18,
    68,
    72,
    108,
    120,
    137,
    179
   ],
   [
    18,
    19,
    73,
    84,
    109,
    121,
    153,
    195
   ],
   [
    19,
    20,
    74,
    85,
    110,
    122,
    154,
    196
   ],
   [
    5,
    21,
    71,
    75,
    111,
    123,
    134,
    176
   ],
   [
    21,
    22,
    76,
    87,
    112,
    124,
    150,
    192
   ],
   [
    22,
    23,
    77,
    88,
    113,
    125,
    151,
    193
   ],
   [
    8,
    24,
    74,
    78,
    114,
    126,
    143,
    185
   ],
   [
    24,
    25,
    79,
    90,
    115,
    127,
    159,
    200
   ],
   [
    25,
    26,
    80,
    91,
    116,
    128,
    160,
    201
   ],
   [
    11,
    27,
    77,
    81,
    117,
    129,
    140,
    182
   ],
   [
    27,
    28,
    82,
    93,
    118,
    130,
    156,
    198
   ],
   [
    28,
    29,
    83,
    94,
    119,
    131,
    157,
    199
   ],
   [
    14,
    30,
    80,
    84,
    120,
    132,
    149,
    191
   ],
   [
    30,
    31,
    85,
    96,
    121,
    133,
    165,
    203
   ],
   [
    31,
    32,
    86,
    97,
    106,
    122,
    134,
    166
   ],
   [
    17,
    33,
    83,
    87,
    123,
    135,
    146,
    188
   ],
   [
    33,
    34,
    88,
    98,
    124,
    136,
    162,
    202
   ],
   [
    34,
    35,
    89,
    99,
    104,
    125,
    137,
    163
   ],
   [
    20,
    36,
    86,
    90,
    126,
    138,
    155,
    197
   ],
   [
    36,
    37,
    91,
    100,
    111,
    127,
    139,
    171
   ],
   [
    2,
    37,
    38,
    92,
    112,
    128,
    140,
    172
   ],
   [
    23,
    39,
    89,
    93,
    129,
    141,
    152,
    194
   ],
   [
    39,
    40,
    94,
    101,
    108,
    130,
    142,
    168
   ],
   [
    4,
    40,
    41,
    95,
    109,
    131,
    143,
    169
   ],
   [
    26,
    42,
    92,
    96,
    103,
    132,
    144,
    161
   ],
   [
    6,
    42,
    43,
    97,
    117,
    133,
    145,
    177
   ],
   [
    0,
    7,
    43,
    44,
    118,
    134,
    146,
    178
   ],
   [
    29,
    45,
    95,
    98,
    102,
    135,
    147,
    158
   ],
   [
    9,
    45,
    46,
    99,
    114,
    136,
    148,
    174
   ],
   [
    1,
    10,
    46,
    47,
    115,
    137,
    149,
    175
   ],
   [
    0,
    32,
    48,
    100,
    107,
    138,
    150,
    167
   ],
   [
    2,
    12,
    48,
    49,
    123,
    139,
    151,
    183
   ],
   [
    3,
    13,
    49,
    50,
    124,
    140,
    152,
    184
   ],
   [
    1,
    35,
    51,
    101,
    105,
    141,
    153,
    164
   ],
   [
    4,
    15,
    51,
    52,
    120,
    142,
    154,
    180
   ],
   [
    5,
    16,
    52,
    53,
    121,
    143,
    155,
    181
   ],
   [
    3,
    6,
    38,
    54,
    113,
    144,
    156,
    173
   ],
   [
    7,
    18,
    54,
    55,
    129,
    145,
    157,
    189
   ],
   [
    8,
    19,
    55,
    56,
    130,
    146,
    158,
    190
   ],
   [
    5,
    9,
    41,
    57,
    110,
    147,
    159,
    170
   ],
   [
    10,
    21,
    57,
    58,
    126,
    148,
    160,
    186
   ],
   [
    11,
    22,
    58,
    59,
    127,
    149,
    161,
    187
   ],
   [
    8,
    12,
    44,
    60,
    119,
    150,
    162,
    179
   ],
   [
    13,
    24,
    60,
    61,
    135,
    151,
    163,
    195
   ],
   [
    14,
    25,
    61,
    62,
    136,
    152,
    164,
    196
   ],
   [
    11,
    15,
    47,
    63,
    116,
    153,
    165,
    176
   ],
   [
    16,
    27,
    63,
    64,
    132,
    154,
    166,
    192
   ],
   [
    17,
    28,
    64,
    65,
    133,
    155,
    167,
    193
   ],
   [
    14,
    18,
    50,
    66,
    125,
    156,
    168,
    185
   ],
   [
    19,
    30,
    66,
    67,
    141,
    157,
    169,
    200
   ],
   [
    20,
    31,
    67,
    68,
    142,
    158,
    170,
    201
   ],
   [
    17,
    21,
    53,
    69,
    122,
    159,
    171,
    182
   ],
   [
    22,
    33,
    69,
    70,
    138,
    160,
    172,
    198
   ],
   [
    23,
    34,
    70,
    71,
    139,
    161,
    173,
    199
   ],
   [
    20,
    24,
    56,
    72,
    131,
    162,
    174,
    191
   ],
   [
    25,
    36,
    72,
    73,
    147,
    163,
    175,
    203
   ],
   [
    26,
    37,
    73,
    74,
    106,
    148,
    164,
    176
   ],
   [
    23,
    27,
    59,
    75,
    128,
    165,
    177,
    188
   ],
   [
    28,
    39,
    75,
    76,
    144,
    166,
    178,
    202
   ],
   [
    29,
    40,
    76,
    77,
    104,
    145,
    167,
    179
   ],
   [
    26,
    30,
    62,
    78,
    137,
    168,
    180,
    197
   ],
   [
    31,
    42,
    78,
    79,
    111,
    153,
    169,
    181
   ],
   [
    32,
    43,
    79,
    80,
    112,
    154,
    170,
    182
   ],
   [
    29,
    33,
    65,
    81,
    134,
    171,
    183,
    194
   ],
   [
    34,
    45,
    81,
    82,
    108,
    150,
    172,
    184
   ],
   [
    35,
    46,
    82,
    83,
    109,
    151,
    173,
    185
   ],
   [
    32,
    36,
    68,
    84,
    103,
    143,
    174,
    186
   ],
   [
    37,
    48,
    84,
    85,
    117,
    159,
    175,
    187
   ],
   [
    38,
    49,
    85,
    86,
    118,
    160,
    176,
    188
   ],
   [
    35,
    39,
    71,
    87,
    102,
    140,
    177,
    189
   ],
   [
    40,
    51,
    87,
    88,
    114,
    156,
    178,
    190
   ],
   [
    41,
    52,
    88,
    89,
    115,
    157,
    179,
    191
   ],
   [
    38,
    42,
    74,
    90,
    107,
    149,
    180,
    192
   ],
   [
    43,
    54,
    90,
    91,
    123,
    165,
    181,
    193
   ],
   [
    44,
    55,
    91,
    92,
    124,
    166,
    182,
    194
   ],
   [
    41,
    45,
    77,
    93,
    105,
    146,
    183,
    195
   ],
   [
    46,
    57,
    93,
    94,
    120,
    162,
    184,
    196
   ],
   [
    47,
    58,
    94,
    95,
    121,
    163,
    185,
    197
   ],
   [
    44,
    48,
    80,
    96,
    113,
    155,
    186,
    198
   ],
   [
    49,
    60,
    96,
    97,
    129,
    171,
    187,
    199
   ],
   [
    47,
    51,
    83,
    98,
    110,
    152,
    189,
    200
   ],
   [
    52,
    63,
    98,
    99,
    126,
    168,
    190,
    201
   ],
   [
    50,
    54,
    86,
    100,
    119,
    161,
    192,
    202
   ],
   [
    53,
    57,
    89,
    101,
    116,
    158,
    195,
    203
   ]
  ]
 },
 "distance": {
  "d": 12,
  "X": {
   "value": 12,
   "confidence": "upper_bound",
   "witness": [
    14,
    47,
    57,
    58,
    110,
    116,
    142,
    149,
    168,
    180,
    196,
    201
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1021
    ]
   }
  },
  "Z": {
   "value": 12,
   "confidence": "upper_bound",
   "witness": [
    1,
    16,
    30,
    42,
    53,
    59,
    79,
    85,
    121,
    154,
    155,
    159
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1022
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C102 = SmallGroup(102, 4) (order 102), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 204; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 28, 70, 86}, b = {0, 50, 61, 97} as element indices. Check weight 8. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race.",
  "references": [
   "arXiv:2610.13880"
  ],
  "date": "2026-10-12",
  "notes": "Parameters and construction taken from the public database of arXiv:2610.13880v1. Distance is an upper bound certified by the witnesses attached here. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race @ aed705a, CC BY 4.0; rebuilt here with the repo's own group data. Distance is an upper bound certified by the attached witnesses, not the paper's exact distance.",
  "origin": "baseline",
  "novelty": "known_parameters",
  "model": "Mimo-V2.6-Flash"
 },
 "family": "generalized-bicycle"
}