{
 "schema_version": "0.2",
 "name": "[[120,16,10]] two-block code over C30 x C2",
 "code_type": "CSS",
 "n": 120,
 "k": 16,
 "checks": {
  "X": [
   [
    0,
    15,
    43,
    59,
    60,
    87,
    118
   ],
   [
    1,
    10,
    48,
    58,
    61,
    81,
    119
   ],
   [
    2,
    24,
    34,
    57,
    62,
    96,
    114
   ],
   [
    1,
    3,
    49,
    52,
    63,
    67,
    104
   ],
   [
    4,
    24,
    27,
    53,
    64,
    78,
    99
   ],
   [
    5,
    18,
    40,
    54,
    65,
    90,
    117
   ],
   [
    0,
    6,
    44,
    55,
    64,
    66,
    109
   ],
   [
    7,
    18,
    21,
    56,
    67,
    84,
    93
   ],
   [
    5,
    8,
    41,
    45,
    68,
    74,
    95
   ],
   [
    9,
    15,
    36,
    46,
    69,
    70,
    107
   ],
   [
    6,
    10,
    32,
    56,
    70,
    76,
    113
   ],
   [
    5,
    7,
    11,
    58,
    62,
    71,
    77
   ],
   [
    8,
    12,
    36,
    39,
    72,
    90,
    110
   ],
   [
    2,
    13,
    35,
    50,
    69,
    73,
    101
   ],
   [
    10,
    14,
    30,
    51,
    74,
    75,
    102
   ],
   [
    3,
    15,
    38,
    53,
    71,
    75,
    116
   ],
   [
    2,
    4,
    16,
    59,
    65,
    72,
    76
   ],
   [
    13,
    17,
    30,
    33,
    77,
    96,
    105
   ],
   [
    13,
    18,
    23,
    51,
    78,
    85,
    106
   ],
   [
    1,
    14,
    19,
    54,
    60,
    79,
    86
   ],
   [
    3,
    20,
    27,
    47,
    80,
    81,
    115
   ],
   [
    13,
    16,
    21,
    44,
    68,
    81,
    88
   ],
   [
    14,
    17,
    18,
    22,
    69,
    82,
    89
   ],
   [
    19,
    23,
    47,
    50,
    83,
    102,
    117
   ],
   [
    8,
    24,
    29,
    46,
    79,
    84,
    111
   ],
   [
    0,
    9,
    25,
    57,
    61,
    80,
    85
   ],
   [
    6,
    21,
    26,
    42,
    86,
    87,
    112
   ],
   [
    8,
    11,
    27,
    49,
    73,
    82,
    87
   ],
   [
    9,
    12,
    24,
    28,
    74,
    83,
    88
   ],
   [
    25,
    29,
    42,
    45,
    89,
    107,
    114
   ],
   [
    6,
    25,
    30,
    35,
    63,
    90,
    97
   ],
   [
    7,
    10,
    26,
    31,
    64,
    91,
    98
   ],
   [
    11,
    32,
    39,
    55,
    92,
    93,
    119
   ],
   [
    2,
    25,
    28,
    33,
    79,
    93,
    100
   ],
   [
    26,
    29,
    30,
    34,
    80,
    94,
    101
   ],
   [
    31,
    35,
    55,
    57,
    75,
    95,
    112
   ],
   [
    3,
    19,
    36,
    41,
    66,
    91,
    96
   ],
   [
    4,
    15,
    20,
    37,
    67,
    92,
    97
   ],
   [
    16,
    33,
    38,
    52,
    98,
    99,
    118
   ],
   [
    5,
    19,
    22,
    39,
    85,
    94,
    99
   ],
   [
    20,
    23,
    36,
    40,
    86,
    95,
    100
   ],
   [
    37,
    41,
    52,
    54,
    70,
    101,
    115
   ],
   [
    0,
    16,
    37,
    42,
    71,
    102,
    108
   ],
   [
    17,
    21,
    38,
    43,
    72,
    103,
    109
   ],
   [
    22,
    44,
    50,
    59,
    84,
    104,
    105
   ],
   [
    9,
    37,
    40,
    45,
    91,
    105,
    111
   ],
   [
    38,
    41,
    42,
    46,
    61,
    92,
    106
   ],
   [
    1,
    11,
    31,
    47,
    76,
    103,
    107
   ],
   [
    12,
    27,
    32,
    48,
    77,
    104,
    108
   ],
   [
    28,
    45,
    49,
    58,
    78,
    109,
    110
   ],
   [
    14,
    31,
    34,
    50,
    97,
    106,
    110
   ],
   [
    32,
    35,
    47,
    51,
    60,
    98,
    111
   ],
   [
    4,
    28,
    48,
    52,
    82,
    112,
    116
   ],
   [
    29,
    33,
    49,
    53,
    65,
    83,
    113
   ],
   [
    20,
    48,
    51,
    54,
    66,
    103,
    114
   ],
   [
    7,
    22,
    43,
    55,
    88,
    113,
    115
   ],
   [
    23,
    39,
    44,
    56,
    62,
    89,
    116
   ],
   [
    26,
    43,
    46,
    57,
    63,
    108,
    117
   ],
   [
    12,
    40,
    56,
    58,
    73,
    94,
    118
   ],
   [
    17,
    34,
    53,
    59,
    68,
    100,
    119
   ]
  ],
  "Z": [
   [
    0,
    19,
    51,
    60,
    66,
    85,
    102
   ],
   [
    1,
    25,
    46,
    61,
    63,
    79,
    107
   ],
   [
    2,
    11,
    56,
    62,
    73,
    76,
    93
   ],
   [
    3,
    30,
    57,
    63,
    75,
    80,
    96
   ],
   [
    4,
    6,
    31,
    64,
    76,
    97,
    112
   ],
   [
    5,
    16,
    53,
    65,
    68,
    71,
    99
   ],
   [
    6,
    36,
    54,
    66,
    70,
    86,
    90
   ],
   [
    3,
    7,
    37,
    67,
    71,
    91,
    115
   ],
   [
    8,
    21,
    59,
    68,
    72,
    84,
    87
   ],
   [
    9,
    13,
    22,
    69,
    85,
    88,
    105
   ],
   [
    9,
    10,
    41,
    61,
    70,
    74,
    91
   ],
   [
    11,
    15,
    42,
    71,
    87,
    92,
    107
   ],
   [
    12,
    16,
    43,
    72,
    88,
    108,
    118
   ],
   [
    13,
    27,
    58,
    73,
    77,
    78,
    81
   ],
   [
    8,
    14,
    28,
    74,
    79,
    82,
    110
   ],
   [
    14,
    15,
    35,
    60,
    69,
    75,
    97
   ],
   [
    10,
    16,
    47,
    76,
    81,
    98,
    102
   ],
   [
    11,
    17,
    48,
    77,
    82,
    103,
    119
   ],
   [
    4,
    18,
    49,
    65,
    67,
    78,
    82
   ],
   [
    19,
    24,
    33,
    79,
    83,
    96,
    99
   ],
   [
    20,
    25,
    34,
    80,
    97,
    100,
    114
   ],
   [
    1,
    20,
    21,
    67,
    81,
    86,
    103
   ],
   [
    22,
    27,
    52,
    82,
    99,
    104,
    115
   ],
   [
    23,
    28,
    53,
    78,
    83,
    100,
    116
   ],
   [
    7,
    24,
    44,
    62,
    64,
    84,
    88
   ],
   [
    18,
    25,
    39,
    85,
    89,
    90,
    93
   ],
   [
    19,
    26,
    40,
    86,
    91,
    94,
    117
   ],
   [
    0,
    26,
    27,
    64,
    80,
    87,
    108
   ],
   [
    21,
    28,
    55,
    88,
    93,
    109,
    112
   ],
   [
    22,
    29,
    56,
    84,
    89,
    94,
    113
   ],
   [
    5,
    12,
    30,
    74,
    77,
    90,
    94
   ],
   [
    31,
    36,
    45,
    91,
    95,
    107,
    110
   ],
   [
    32,
    37,
    46,
    70,
    92,
    108,
    111
   ],
   [
    7,
    32,
    33,
    77,
    93,
    98,
    113
   ],
   [
    34,
    39,
    58,
    62,
    94,
    110,
    119
   ],
   [
    8,
    35,
    40,
    73,
    90,
    95,
    111
   ],
   [
    2,
    17,
    36,
    69,
    72,
    96,
    100
   ],
   [
    30,
    37,
    50,
    97,
    101,
    102,
    105
   ],
   [
    31,
    38,
    51,
    75,
    98,
    103,
    106
   ],
   [
    4,
    38,
    39,
    72,
    92,
    99,
    116
   ],
   [
    33,
    40,
    59,
    65,
    100,
    105,
    118
   ],
   [
    13,
    34,
    41,
    68,
    96,
    101,
    106
   ],
   [
    14,
    23,
    42,
    86,
    89,
    102,
    106
   ],
   [
    43,
    47,
    54,
    60,
    103,
    115,
    117
   ],
   [
    3,
    44,
    48,
    66,
    81,
    104,
    116
   ],
   [
    17,
    44,
    45,
    68,
    89,
    105,
    109
   ],
   [
    18,
    46,
    50,
    69,
    84,
    106,
    117
   ],
   [
    9,
    29,
    47,
    80,
    83,
    107,
    111
   ],
   [
    42,
    48,
    57,
    61,
    108,
    112,
    114
   ],
   [
    6,
    43,
    49,
    63,
    87,
    109,
    113
   ],
   [
    12,
    49,
    50,
    73,
    83,
    104,
    110
   ],
   [
    24,
    45,
    51,
    74,
    78,
    111,
    114
   ],
   [
    26,
    35,
    52,
    63,
    98,
    101,
    112
   ],
   [
    10,
    53,
    55,
    64,
    75,
    113,
    119
   ],
   [
    2,
    29,
    54,
    65,
    79,
    101,
    114
   ],
   [
    20,
    41,
    55,
    66,
    92,
    95,
    115
   ],
   [
    15,
    52,
    56,
    67,
    70,
    116,
    118
   ],
   [
    5,
    23,
    57,
    62,
    85,
    95,
    117
   ],
   [
    0,
    38,
    58,
    61,
    71,
    109,
    118
   ],
   [
    1,
    32,
    59,
    60,
    76,
    104,
    119
   ]
  ]
 },
 "distance": {
  "d": 10,
  "X": {
   "value": 10,
   "confidence": "upper_bound",
   "witness": [
    16,
    27,
    38,
    48,
    71,
    81,
    92,
    103,
    108,
    115
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1024
    ]
   }
  },
  "Z": {
   "value": 10,
   "confidence": "upper_bound",
   "witness": [
    6,
    21,
    38,
    44,
    46,
    52,
    63,
    70,
    84,
    116
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1025
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C30 x C2 = SmallGroup(60, 13) (order 60), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 120; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 6, 25, 42}, b = {0, 19, 51} as element indices. Check weight 7. 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"
}
