{
 "schema_version": "0.2",
 "name": "[[224,18,12]] two-block code over C7 x (C4 : C4)",
 "code_type": "CSS",
 "n": 224,
 "k": 18,
 "checks": {
  "X": [
   [
    0,
    73,
    100,
    112,
    143,
    189
   ],
   [
    1,
    64,
    76,
    113,
    151,
    197
   ],
   [
    2,
    44,
    107,
    114,
    155,
    201
   ],
   [
    3,
    9,
    89,
    115,
    159,
    204
   ],
   [
    4,
    56,
    109,
    116,
    127,
    172
   ],
   [
    5,
    84,
    91,
    117,
    126,
    206
   ],
   [
    6,
    69,
    88,
    118,
    163,
    208
   ],
   [
    0,
    7,
    80,
    119,
    167,
    211
   ],
   [
    8,
    81,
    92,
    120,
    134,
    180
   ],
   [
    9,
    82,
    93,
    121,
    133,
    213
   ],
   [
    10,
    19,
    60,
    122,
    171,
    214
   ],
   [
    11,
    61,
    111,
    123,
    138,
    184
   ],
   [
    12,
    62,
    95,
    124,
    137,
    216
   ],
   [
    13,
    22,
    102,
    116,
    125,
    175
   ],
   [
    14,
    23,
    72,
    126,
    142,
    188
   ],
   [
    1,
    15,
    104,
    127,
    141,
    217
   ],
   [
    16,
    74,
    99,
    115,
    128,
    190
   ],
   [
    2,
    17,
    85,
    129,
    179,
    218
   ],
   [
    18,
    52,
    102,
    130,
    146,
    192
   ],
   [
    19,
    87,
    103,
    131,
    145,
    220
   ],
   [
    3,
    20,
    95,
    120,
    132,
    183
   ],
   [
    4,
    21,
    96,
    133,
    150,
    196
   ],
   [
    5,
    22,
    97,
    134,
    149,
    221
   ],
   [
    23,
    98,
    105,
    119,
    135,
    198
   ],
   [
    24,
    34,
    76,
    123,
    136,
    187
   ],
   [
    25,
    35,
    77,
    137,
    154,
    200
   ],
   [
    6,
    26,
    78,
    138,
    153,
    222
   ],
   [
    27,
    79,
    106,
    122,
    139,
    202
   ],
   [
    11,
    28,
    38,
    126,
    140,
    191
   ],
   [
    29,
    39,
    88,
    112,
    141,
    158
   ],
   [
    7,
    30,
    110,
    128,
    142,
    157
   ],
   [
    8,
    31,
    90,
    125,
    143,
    205
   ],
   [
    10,
    32,
    99,
    130,
    144,
    195
   ],
   [
    11,
    33,
    68,
    145,
    162,
    207
   ],
   [
    12,
    34,
    101,
    146,
    161,
    223
   ],
   [
    35,
    70,
    110,
    129,
    147,
    209
   ],
   [
    6,
    13,
    36,
    133,
    148,
    199
   ],
   [
    14,
    37,
    106,
    113,
    149,
    166
   ],
   [
    15,
    38,
    107,
    135,
    150,
    165
   ],
   [
    16,
    39,
    108,
    132,
    151,
    212
   ],
   [
    0,
    40,
    50,
    137,
    152,
    203
   ],
   [
    41,
    51,
    92,
    114,
    153,
    170
   ],
   [
    17,
    42,
    93,
    139,
    154,
    169
   ],
   [
    18,
    43,
    94,
    136,
    155,
    215
   ],
   [
    25,
    44,
    54,
    141,
    156,
    206
   ],
   [
    2,
    45,
    55,
    115,
    157,
    174
   ],
   [
    20,
    27,
    46,
    143,
    158,
    173
   ],
   [
    21,
    47,
    103,
    117,
    140,
    159
   ],
   [
    8,
    24,
    48,
    145,
    160,
    210
   ],
   [
    25,
    49,
    84,
    118,
    161,
    178
   ],
   [
    26,
    50,
    109,
    147,
    162,
    177
   ],
   [
    27,
    51,
    86,
    144,
    163,
    219
   ],
   [
    17,
    28,
    52,
    149,
    164,
    213
   ],
   [
    18,
    29,
    53,
    119,
    165,
    182
   ],
   [
    19,
    30,
    54,
    151,
    166,
    181
   ],
   [
    31,
    55,
    111,
    121,
    148,
    167
   ],
   [
    3,
    56,
    66,
    153,
    168,
    216
   ],
   [
    4,
    57,
    67,
    122,
    169,
    186
   ],
   [
    5,
    32,
    58,
    155,
    170,
    185
   ],
   [
    33,
    59,
    105,
    124,
    152,
    171
   ],
   [
    41,
    60,
    70,
    157,
    172,
    217
   ],
   [
    10,
    61,
    71,
    125,
    173,
    190
   ],
   [
    36,
    43,
    62,
    159,
    174,
    189
   ],
   [
    12,
    37,
    63,
    127,
    156,
    175
   ],
   [
    21,
    40,
    64,
    161,
    176,
    220
   ],
   [
    1,
    41,
    65,
    129,
    177,
    194
   ],
   [
    23,
    42,
    66,
    163,
    178,
    193
   ],
   [
    43,
    67,
    100,
    131,
    160,
    179
   ],
   [
    32,
    44,
    68,
    165,
    180,
    221
   ],
   [
    33,
    45,
    69,
    132,
    181,
    198
   ],
   [
    34,
    46,
    70,
    167,
    182,
    197
   ],
   [
    35,
    47,
    71,
    134,
    164,
    183
   ],
   [
    13,
    72,
    82,
    169,
    184,
    222
   ],
   [
    14,
    73,
    83,
    136,
    185,
    202
   ],
   [
    15,
    48,
    74,
    171,
    186,
    201
   ],
   [
    16,
    49,
    75,
    138,
    168,
    187
   ],
   [
    57,
    76,
    86,
    128,
    173,
    188
   ],
   [
    24,
    77,
    87,
    140,
    189,
    205
   ],
   [
    52,
    59,
    78,
    175,
    190,
    204
   ],
   [
    26,
    53,
    79,
    142,
    172,
    191
   ],
   [
    37,
    56,
    80,
    177,
    192,
    223
   ],
   [
    7,
    57,
    81,
    144,
    193,
    209
   ],
   [
    39,
    58,
    82,
    179,
    194,
    208
   ],
   [
    9,
    59,
    83,
    146,
    176,
    195
   ],
   [
    48,
    60,
    84,
    135,
    181,
    196
   ],
   [
    49,
    61,
    85,
    148,
    197,
    212
   ],
   [
    50,
    62,
    86,
    183,
    198,
    211
   ],
   [
    51,
    63,
    87,
    150,
    180,
    199
   ],
   [
    28,
    88,
    97,
    139,
    185,
    200
   ],
   [
    29,
    89,
    98,
    152,
    201,
    215
   ],
   [
    30,
    64,
    90,
    187,
    202,
    214
   ],
   [
    31,
    65,
    91,
    154,
    184,
    203
   ],
   [
    40,
    92,
    101,
    117,
    156,
    204
   ],
   [
    68,
    75,
    93,
    116,
    191,
    205
   ],
   [
    42,
    69,
    94,
    158,
    188,
    206
   ],
   [
    53,
    72,
    95,
    147,
    193,
    207
   ],
   [
    20,
    73,
    96,
    160,
    208,
    219
   ],
   [
    55,
    74,
    97,
    195,
    209,
    218
   ],
   [
    22,
    75,
    98,
    162,
    192,
    210
   ],
   [
    65,
    77,
    99,
    121,
    164,
    211
   ],
   [
    66,
    78,
    100,
    120,
    199,
    212
   ],
   [
    67,
    79,
    101,
    166,
    196,
    213
   ],
   [
    45,
    102,
    108,
    124,
    168,
    214
   ],
   [
    46,
    80,
    103,
    123,
    203,
    215
   ],
   [
    47,
    81,
    104,
    170,
    200,
    216
   ],
   [
    58,
    85,
    105,
    112,
    174,
    217
   ],
   [
    36,
    89,
    106,
    131,
    176,
    218
   ],
   [
    71,
    90,
    107,
    130,
    210,
    219
   ],
   [
    38,
    91,
    108,
    178,
    207,
    220
   ],
   [
    83,
    94,
    109,
    113,
    182,
    221
   ],
   [
    63,
    96,
    110,
    114,
    186,
    222
   ],
   [
    54,
    104,
    111,
    118,
    194,
    223
   ]
  ],
  "Z": [
   [
    0,
    29,
    105,
    112,
    119,
    152
   ],
   [
    1,
    37,
    109,
    113,
    127,
    177
   ],
   [
    2,
    41,
    110,
    114,
    129,
    157
   ],
   [
    3,
    16,
    45,
    115,
    132,
    168
   ],
   [
    4,
    13,
    93,
    116,
    133,
    169
   ],
   [
    5,
    47,
    92,
    117,
    134,
    170
   ],
   [
    6,
    49,
    111,
    118,
    138,
    148
   ],
   [
    7,
    23,
    53,
    119,
    142,
    193
   ],
   [
    8,
    20,
    100,
    120,
    143,
    160
   ],
   [
    9,
    55,
    99,
    115,
    121,
    195
   ],
   [
    10,
    27,
    57,
    122,
    144,
    173
   ],
   [
    11,
    24,
    103,
    123,
    140,
    145
   ],
   [
    12,
    59,
    102,
    124,
    146,
    175
   ],
   [
    13,
    31,
    61,
    125,
    148,
    184
   ],
   [
    5,
    14,
    28,
    126,
    149,
    185
   ],
   [
    4,
    15,
    63,
    127,
    150,
    186
   ],
   [
    16,
    30,
    76,
    128,
    151,
    187
   ],
   [
    17,
    35,
    65,
    129,
    154,
    164
   ],
   [
    18,
    32,
    107,
    130,
    155,
    165
   ],
   [
    19,
    67,
    106,
    122,
    131,
    166
   ],
   [
    20,
    39,
    69,
    132,
    158,
    208
   ],
   [
    9,
    21,
    36,
    133,
    159,
    176
   ],
   [
    8,
    22,
    71,
    125,
    134,
    210
   ],
   [
    23,
    38,
    84,
    126,
    135,
    178
   ],
   [
    24,
    43,
    73,
    136,
    160,
    189
   ],
   [
    12,
    25,
    40,
    137,
    156,
    161
   ],
   [
    11,
    26,
    75,
    138,
    162,
    191
   ],
   [
    27,
    42,
    88,
    139,
    158,
    163
   ],
   [
    28,
    47,
    77,
    140,
    164,
    200
   ],
   [
    15,
    29,
    44,
    141,
    165,
    201
   ],
   [
    14,
    30,
    79,
    142,
    166,
    202
   ],
   [
    0,
    31,
    46,
    143,
    167,
    203
   ],
   [
    32,
    51,
    81,
    144,
    170,
    180
   ],
   [
    19,
    33,
    48,
    145,
    171,
    181
   ],
   [
    18,
    34,
    83,
    136,
    146,
    182
   ],
   [
    35,
    50,
    95,
    137,
    147,
    183
   ],
   [
    36,
    55,
    85,
    148,
    174,
    218
   ],
   [
    22,
    37,
    52,
    149,
    175,
    192
   ],
   [
    21,
    38,
    87,
    140,
    150,
    220
   ],
   [
    1,
    39,
    54,
    141,
    151,
    194
   ],
   [
    40,
    59,
    89,
    152,
    176,
    204
   ],
   [
    26,
    41,
    56,
    153,
    172,
    177
   ],
   [
    25,
    42,
    91,
    154,
    178,
    206
   ],
   [
    2,
    43,
    58,
    155,
    174,
    179
   ],
   [
    44,
    63,
    92,
    114,
    156,
    180
   ],
   [
    30,
    45,
    60,
    157,
    181,
    214
   ],
   [
    29,
    46,
    94,
    158,
    182,
    215
   ],
   [
    3,
    47,
    62,
    159,
    183,
    216
   ],
   [
    48,
    67,
    96,
    160,
    186,
    196
   ],
   [
    34,
    49,
    64,
    161,
    187,
    197
   ],
   [
    33,
    50,
    98,
    152,
    162,
    198
   ],
   [
    6,
    51,
    66,
    153,
    163,
    199
   ],
   [
    52,
    71,
    99,
    130,
    164,
    190
   ],
   [
    38,
    53,
    68,
    165,
    191,
    207
   ],
   [
    37,
    54,
    101,
    156,
    166,
    223
   ],
   [
    7,
    55,
    70,
    157,
    167,
    209
   ],
   [
    56,
    75,
    102,
    116,
    168,
    192
   ],
   [
    42,
    57,
    72,
    169,
    188,
    193
   ],
   [
    41,
    58,
    104,
    170,
    194,
    217
   ],
   [
    10,
    59,
    74,
    171,
    190,
    195
   ],
   [
    4,
    60,
    79,
    122,
    172,
    196
   ],
   [
    46,
    61,
    76,
    123,
    173,
    197
   ],
   [
    45,
    62,
    105,
    124,
    174,
    198
   ],
   [
    13,
    63,
    78,
    175,
    199,
    222
   ],
   [
    64,
    83,
    106,
    113,
    176,
    202
   ],
   [
    50,
    65,
    80,
    177,
    203,
    211
   ],
   [
    49,
    66,
    108,
    168,
    178,
    212
   ],
   [
    17,
    67,
    82,
    169,
    179,
    213
   ],
   [
    8,
    68,
    87,
    145,
    180,
    205
   ],
   [
    54,
    69,
    84,
    118,
    181,
    206
   ],
   [
    53,
    70,
    109,
    147,
    172,
    182
   ],
   [
    20,
    71,
    86,
    173,
    183,
    219
   ],
   [
    11,
    72,
    91,
    126,
    184,
    207
   ],
   [
    58,
    73,
    88,
    112,
    185,
    208
   ],
   [
    57,
    74,
    110,
    128,
    186,
    209
   ],
   [
    24,
    75,
    90,
    187,
    205,
    210
   ],
   [
    14,
    76,
    94,
    113,
    136,
    188
   ],
   [
    0,
    62,
    77,
    137,
    189,
    211
   ],
   [
    16,
    61,
    78,
    138,
    190,
    212
   ],
   [
    28,
    79,
    93,
    139,
    191,
    213
   ],
   [
    18,
    80,
    98,
    119,
    192,
    215
   ],
   [
    66,
    81,
    95,
    120,
    193,
    216
   ],
   [
    65,
    82,
    111,
    121,
    184,
    194
   ],
   [
    32,
    83,
    97,
    185,
    195,
    221
   ],
   [
    21,
    84,
    101,
    117,
    161,
    196
   ],
   [
    1,
    70,
    85,
    129,
    197,
    217
   ],
   [
    23,
    69,
    86,
    163,
    188,
    198
   ],
   [
    36,
    87,
    100,
    131,
    189,
    199
   ],
   [
    25,
    88,
    104,
    118,
    141,
    200
   ],
   [
    2,
    74,
    89,
    115,
    201,
    218
   ],
   [
    27,
    73,
    90,
    143,
    202,
    219
   ],
   [
    40,
    91,
    103,
    117,
    203,
    220
   ],
   [
    3,
    78,
    92,
    120,
    153,
    204
   ],
   [
    31,
    77,
    93,
    121,
    154,
    205
   ],
   [
    5,
    44,
    94,
    155,
    206,
    221
   ],
   [
    33,
    95,
    108,
    124,
    132,
    207
   ],
   [
    6,
    82,
    96,
    133,
    208,
    222
   ],
   [
    35,
    81,
    97,
    134,
    200,
    209
   ],
   [
    48,
    98,
    107,
    135,
    201,
    210
   ],
   [
    7,
    86,
    99,
    128,
    144,
    211
   ],
   [
    39,
    85,
    100,
    112,
    179,
    212
   ],
   [
    9,
    52,
    101,
    146,
    204,
    213
   ],
   [
    10,
    90,
    102,
    125,
    130,
    214
   ],
   [
    43,
    89,
    103,
    131,
    159,
    215
   ],
   [
    12,
    56,
    104,
    127,
    216,
    223
   ],
   [
    15,
    60,
    105,
    135,
    171,
    217
   ],
   [
    17,
    97,
    106,
    139,
    149,
    218
   ],
   [
    51,
    96,
    107,
    114,
    150,
    219
   ],
   [
    19,
    64,
    108,
    151,
    214,
    220
   ],
   [
    22,
    68,
    109,
    116,
    162,
    221
   ],
   [
    26,
    72,
    110,
    142,
    147,
    222
   ],
   [
    34,
    80,
    111,
    123,
    167,
    223
   ]
  ]
 },
 "distance": {
  "d": 12,
  "X": {
   "value": 12,
   "confidence": "upper_bound",
   "witness": [
    19,
    33,
    35,
    50,
    51,
    65,
    66,
    67,
    81,
    82,
    96,
    108
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1029
    ]
   }
  },
  "Z": {
   "value": 12,
   "confidence": "upper_bound",
   "witness": [
    112,
    116,
    125,
    126,
    141,
    143,
    172,
    173,
    188,
    191,
    206,
    217
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1030
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C7 x (C4 : C4) = SmallGroup(112, 21) (order 112), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 224; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 7, 40}, b = {0, 29, 105} as element indices. Check weight 6. 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": "2bga-nonabelian"
}