{
 "schema_version": "0.2",
 "name": "[[160,14,16]] two-block code over C80",
 "code_type": "CSS",
 "n": 160,
 "k": 14,
 "checks": {
  "X": [
   [
    0,
    25,
    39,
    54,
    80,
    103,
    143,
    151
   ],
   [
    0,
    1,
    33,
    62,
    81,
    111,
    137,
    155
   ],
   [
    2,
    41,
    55,
    68,
    82,
    87,
    95,
    118
   ],
   [
    1,
    3,
    26,
    69,
    83,
    119,
    144,
    152
   ],
   [
    4,
    7,
    17,
    44,
    81,
    84,
    154,
    158
   ],
   [
    5,
    21,
    34,
    45,
    85,
    88,
    136,
    155
   ],
   [
    2,
    6,
    49,
    73,
    84,
    86,
    102,
    127
   ],
   [
    3,
    7,
    10,
    34,
    80,
    87,
    150,
    156
   ],
   [
    4,
    8,
    25,
    52,
    83,
    88,
    138,
    159
   ],
   [
    5,
    9,
    44,
    53,
    89,
    94,
    143,
    152
   ],
   [
    10,
    56,
    69,
    76,
    90,
    98,
    109,
    134
   ],
   [
    6,
    11,
    42,
    77,
    88,
    91,
    96,
    135
   ],
   [
    12,
    18,
    32,
    59,
    86,
    92,
    101,
    111
   ],
   [
    13,
    36,
    50,
    60,
    83,
    93,
    99,
    102
   ],
   [
    8,
    14,
    27,
    33,
    87,
    94,
    120,
    145
   ],
   [
    9,
    15,
    46,
    52,
    95,
    101,
    137,
    156
   ],
   [
    16,
    22,
    35,
    62,
    89,
    96,
    150,
    159
   ],
   [
    10,
    17,
    63,
    78,
    92,
    97,
    117,
    142
   ],
   [
    11,
    18,
    24,
    50,
    82,
    94,
    98,
    103
   ],
   [
    12,
    19,
    41,
    66,
    85,
    91,
    99,
    119
   ],
   [
    13,
    20,
    59,
    67,
    87,
    96,
    100,
    108
   ],
   [
    14,
    21,
    26,
    35,
    84,
    101,
    128,
    151
   ],
   [
    15,
    22,
    27,
    54,
    85,
    102,
    144,
    158
   ],
   [
    16,
    23,
    45,
    69,
    95,
    103,
    120,
    154
   ],
   [
    3,
    23,
    24,
    77,
    104,
    113,
    125,
    148
   ],
   [
    17,
    25,
    57,
    79,
    99,
    105,
    110,
    149
   ],
   [
    26,
    33,
    48,
    70,
    97,
    106,
    116,
    127
   ],
   [
    27,
    52,
    64,
    71,
    91,
    107,
    114,
    117
   ],
   [
    19,
    28,
    43,
    49,
    80,
    89,
    98,
    108
   ],
   [
    20,
    29,
    61,
    66,
    84,
    103,
    109,
    116
   ],
   [
    30,
    37,
    51,
    73,
    94,
    100,
    110,
    119
   ],
   [
    10,
    23,
    31,
    53,
    102,
    111,
    128,
    138
   ],
   [
    7,
    24,
    31,
    32,
    106,
    112,
    133,
    153
   ],
   [
    25,
    33,
    40,
    64,
    90,
    108,
    113,
    118
   ],
   [
    26,
    34,
    56,
    74,
    93,
    105,
    114,
    135
   ],
   [
    27,
    35,
    70,
    75,
    98,
    110,
    115,
    124
   ],
   [
    28,
    36,
    42,
    51,
    81,
    92,
    95,
    116
   ],
   [
    29,
    37,
    43,
    68,
    88,
    93,
    111,
    117
   ],
   [
    30,
    38,
    60,
    77,
    80,
    101,
    109,
    118
   ],
   [
    17,
    31,
    39,
    46,
    96,
    119,
    136,
    145
   ],
   [
    11,
    38,
    40,
    79,
    120,
    129,
    140,
    156
   ],
   [
    4,
    32,
    39,
    41,
    114,
    121,
    126,
    157
   ],
   [
    1,
    14,
    42,
    49,
    112,
    122,
    132,
    142
   ],
   [
    8,
    15,
    43,
    66,
    105,
    123,
    130,
    133
   ],
   [
    34,
    44,
    58,
    63,
    82,
    100,
    113,
    124
   ],
   [
    35,
    45,
    72,
    74,
    92,
    118,
    125,
    132
   ],
   [
    46,
    53,
    65,
    78,
    108,
    115,
    126,
    135
   ],
   [
    24,
    38,
    47,
    67,
    81,
    85,
    117,
    127
   ],
   [
    18,
    40,
    47,
    48,
    122,
    128,
    147,
    158
   ],
   [
    0,
    8,
    41,
    49,
    104,
    124,
    129,
    134
   ],
   [
    3,
    21,
    42,
    50,
    107,
    121,
    130,
    149
   ],
   [
    14,
    22,
    43,
    51,
    113,
    126,
    131,
    139
   ],
   [
    44,
    52,
    57,
    65,
    86,
    106,
    109,
    132
   ],
   [
    45,
    53,
    58,
    76,
    99,
    107,
    127,
    133
   ],
   [
    46,
    54,
    71,
    79,
    82,
    116,
    125,
    134
   ],
   [
    32,
    47,
    55,
    61,
    83,
    89,
    110,
    135
   ],
   [
    12,
    48,
    55,
    56,
    130,
    136,
    141,
    159
   ],
   [
    6,
    28,
    57,
    63,
    128,
    137,
    146,
    153
   ],
   [
    19,
    29,
    58,
    74,
    121,
    138,
    144,
    147
   ],
   [
    5,
    7,
    50,
    59,
    90,
    115,
    129,
    139
   ],
   [
    16,
    21,
    51,
    60,
    106,
    134,
    140,
    146
   ],
   [
    9,
    31,
    61,
    67,
    124,
    131,
    141,
    149
   ],
   [
    40,
    54,
    62,
    75,
    86,
    93,
    133,
    142
   ],
   [
    2,
    19,
    56,
    63,
    120,
    139,
    143,
    148
   ],
   [
    11,
    36,
    57,
    64,
    123,
    136,
    144,
    157
   ],
   [
    28,
    37,
    58,
    65,
    129,
    141,
    145,
    150
   ],
   [
    4,
    9,
    59,
    66,
    97,
    122,
    125,
    146
   ],
   [
    5,
    23,
    60,
    67,
    114,
    123,
    142,
    147
   ],
   [
    15,
    39,
    61,
    68,
    90,
    132,
    140,
    148
   ],
   [
    48,
    62,
    69,
    72,
    91,
    100,
    126,
    149
   ],
   [
    13,
    18,
    64,
    70,
    104,
    131,
    143,
    150
   ],
   [
    30,
    36,
    65,
    71,
    122,
    148,
    151,
    154
   ],
   [
    20,
    47,
    72,
    75,
    139,
    145,
    152,
    157
   ],
   [
    0,
    22,
    68,
    73,
    97,
    107,
    147,
    153
   ],
   [
    12,
    20,
    70,
    74,
    112,
    137,
    140,
    154
   ],
   [
    13,
    38,
    71,
    75,
    130,
    138,
    153,
    155
   ],
   [
    29,
    55,
    72,
    76,
    104,
    146,
    151,
    156
   ],
   [
    1,
    16,
    73,
    77,
    105,
    115,
    141,
    157
   ],
   [
    2,
    37,
    76,
    78,
    112,
    123,
    155,
    158
   ],
   [
    6,
    30,
    78,
    79,
    121,
    131,
    152,
    159
   ]
  ],
  "Z": [
   [
    0,
    7,
    28,
    38,
    80,
    81,
    129,
    153
   ],
   [
    1,
    4,
    36,
    47,
    81,
    83,
    122,
    157
   ],
   [
    2,
    18,
    44,
    54,
    82,
    86,
    143,
    158
   ],
   [
    3,
    8,
    13,
    55,
    83,
    87,
    104,
    130
   ],
   [
    4,
    6,
    21,
    29,
    84,
    88,
    121,
    146
   ],
   [
    5,
    19,
    22,
    47,
    85,
    89,
    139,
    147
   ],
   [
    6,
    12,
    52,
    62,
    86,
    91,
    137,
    159
   ],
   [
    2,
    7,
    14,
    20,
    84,
    87,
    112,
    139
   ],
   [
    5,
    8,
    11,
    37,
    88,
    94,
    123,
    129
   ],
   [
    9,
    16,
    28,
    55,
    89,
    95,
    141,
    146
   ],
   [
    10,
    33,
    59,
    68,
    87,
    90,
    97,
    111
   ],
   [
    11,
    19,
    27,
    69,
    91,
    98,
    120,
    144
   ],
   [
    12,
    17,
    36,
    45,
    92,
    99,
    136,
    154
   ],
   [
    13,
    34,
    37,
    62,
    93,
    100,
    150,
    155
   ],
   [
    9,
    14,
    18,
    30,
    94,
    101,
    122,
    131
   ],
   [
    2,
    15,
    23,
    36,
    95,
    102,
    123,
    148
   ],
   [
    11,
    16,
    20,
    39,
    96,
    103,
    140,
    157
   ],
   [
    17,
    26,
    66,
    73,
    84,
    97,
    105,
    119
   ],
   [
    10,
    18,
    28,
    35,
    92,
    98,
    128,
    150
   ],
   [
    13,
    19,
    25,
    53,
    99,
    108,
    138,
    143
   ],
   [
    20,
    30,
    44,
    69,
    100,
    109,
    152,
    154
   ],
   [
    12,
    15,
    21,
    38,
    85,
    101,
    130,
    140
   ],
   [
    6,
    13,
    22,
    31,
    96,
    102,
    131,
    153
   ],
   [
    0,
    18,
    23,
    29,
    103,
    104,
    111,
    147
   ],
   [
    24,
    49,
    70,
    76,
    98,
    104,
    112,
    127
   ],
   [
    25,
    34,
    43,
    77,
    80,
    88,
    105,
    113
   ],
   [
    26,
    32,
    52,
    60,
    83,
    101,
    106,
    114
   ],
   [
    27,
    50,
    53,
    73,
    94,
    102,
    107,
    115
   ],
   [
    20,
    28,
    33,
    46,
    108,
    116,
    137,
    145
   ],
   [
    10,
    29,
    38,
    52,
    109,
    117,
    138,
    156
   ],
   [
    25,
    30,
    35,
    55,
    110,
    118,
    151,
    159
   ],
   [
    1,
    12,
    31,
    37,
    111,
    112,
    119,
    141
   ],
   [
    32,
    42,
    74,
    78,
    92,
    112,
    121,
    135
   ],
   [
    24,
    33,
    44,
    51,
    81,
    94,
    106,
    113
   ],
   [
    27,
    34,
    41,
    67,
    85,
    87,
    114,
    124
   ],
   [
    35,
    46,
    59,
    77,
    96,
    101,
    115,
    125
   ],
   [
    26,
    29,
    36,
    54,
    93,
    116,
    144,
    151
   ],
   [
    17,
    27,
    37,
    47,
    110,
    117,
    145,
    158
   ],
   [
    2,
    33,
    38,
    45,
    118,
    120,
    127,
    155
   ],
   [
    3,
    19,
    30,
    39,
    80,
    119,
    121,
    148
   ],
   [
    14,
    23,
    40,
    63,
    113,
    120,
    128,
    142
   ],
   [
    41,
    50,
    58,
    79,
    82,
    99,
    121,
    129
   ],
   [
    42,
    48,
    66,
    71,
    91,
    116,
    122,
    130
   ],
   [
    43,
    64,
    67,
    78,
    108,
    117,
    123,
    131
   ],
   [
    35,
    44,
    49,
    61,
    84,
    89,
    124,
    132
   ],
   [
    24,
    45,
    54,
    66,
    85,
    103,
    125,
    133
   ],
   [
    41,
    46,
    51,
    69,
    95,
    119,
    126,
    134
   ],
   [
    6,
    26,
    47,
    53,
    127,
    128,
    135,
    152
   ],
   [
    21,
    31,
    48,
    57,
    106,
    128,
    136,
    149
   ],
   [
    40,
    49,
    59,
    65,
    86,
    108,
    122,
    129
   ],
   [
    43,
    50,
    56,
    75,
    93,
    98,
    130,
    139
   ],
   [
    51,
    61,
    70,
    79,
    110,
    116,
    131,
    140
   ],
   [
    42,
    45,
    52,
    68,
    88,
    95,
    107,
    132
   ],
   [
    32,
    43,
    53,
    62,
    89,
    111,
    126,
    133
   ],
   [
    10,
    49,
    54,
    60,
    80,
    102,
    134,
    142
   ],
   [
    11,
    34,
    46,
    55,
    82,
    135,
    136,
    156
   ],
   [
    5,
    39,
    56,
    64,
    90,
    114,
    136,
    143
   ],
   [
    1,
    15,
    57,
    74,
    105,
    132,
    137,
    144
   ],
   [
    8,
    31,
    58,
    75,
    124,
    133,
    138,
    145
   ],
   [
    51,
    59,
    63,
    72,
    92,
    100,
    139,
    146
   ],
   [
    40,
    60,
    68,
    74,
    93,
    118,
    140,
    147
   ],
   [
    56,
    61,
    65,
    77,
    109,
    135,
    141,
    148
   ],
   [
    17,
    42,
    62,
    67,
    81,
    96,
    142,
    149
   ],
   [
    0,
    9,
    63,
    70,
    97,
    124,
    137,
    143
   ],
   [
    3,
    22,
    58,
    64,
    107,
    113,
    144,
    150
   ],
   [
    14,
    39,
    65,
    72,
    126,
    132,
    145,
    151
   ],
   [
    57,
    60,
    66,
    76,
    99,
    109,
    123,
    146
   ],
   [
    48,
    58,
    67,
    73,
    100,
    127,
    141,
    147
   ],
   [
    24,
    63,
    68,
    71,
    82,
    117,
    148,
    153
   ],
   [
    25,
    50,
    61,
    69,
    83,
    90,
    103,
    149
   ],
   [
    7,
    16,
    65,
    70,
    106,
    115,
    150,
    154
   ],
   [
    0,
    21,
    71,
    76,
    107,
    134,
    151,
    155
   ],
   [
    3,
    9,
    72,
    79,
    125,
    149,
    152,
    156
   ],
   [
    32,
    57,
    73,
    75,
    86,
    110,
    153,
    157
   ],
   [
    4,
    23,
    71,
    74,
    114,
    125,
    138,
    154
   ],
   [
    1,
    5,
    75,
    78,
    115,
    142,
    152,
    155
   ],
   [
    7,
    15,
    40,
    76,
    90,
    133,
    156,
    158
   ],
   [
    41,
    64,
    72,
    77,
    91,
    104,
    118,
    157
   ],
   [
    4,
    22,
    48,
    78,
    97,
    126,
    158,
    159
   ],
   [
    8,
    16,
    56,
    79,
    105,
    120,
    134,
    159
   ]
  ]
 },
 "distance": {
  "d": 16,
  "X": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": [
    21,
    36,
    50,
    51,
    55,
    56,
    72,
    77,
    79,
    83,
    88,
    94,
    95,
    101,
    136,
    151
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1017
    ]
   }
  },
  "Z": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": [
    20,
    28,
    30,
    42,
    57,
    65,
    74,
    90,
    108,
    109,
    110,
    115,
    121,
    132,
    135,
    157
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1018
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C80 = SmallGroup(80, 2) (order 80), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 160; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 1, 49, 73}, b = {0, 7, 28, 38} 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"
}
