{
 "schema_version": "0.2",
 "name": "[[126,6,14]] two-block code over C63",
 "code_type": "CSS",
 "n": 126,
 "k": 6,
 "checks": {
  "X": [
   [
    0,
    42,
    55,
    63,
    99,
    124
   ],
   [
    1,
    24,
    48,
    64,
    97,
    125
   ],
   [
    0,
    2,
    60,
    65,
    77,
    108
   ],
   [
    3,
    36,
    51,
    66,
    109,
    111
   ],
   [
    4,
    30,
    53,
    67,
    103,
    105
   ],
   [
    1,
    5,
    33,
    68,
    83,
    106
   ],
   [
    6,
    34,
    56,
    69,
    107,
    116
   ],
   [
    2,
    7,
    62,
    70,
    86,
    116
   ],
   [
    3,
    8,
    45,
    64,
    71,
    117
   ],
   [
    9,
    46,
    58,
    72,
    118,
    119
   ],
   [
    4,
    10,
    39,
    63,
    73,
    112
   ],
   [
    11,
    40,
    59,
    74,
    113,
    114
   ],
   [
    5,
    12,
    42,
    75,
    92,
    114
   ],
   [
    6,
    13,
    43,
    67,
    76,
    115
   ],
   [
    14,
    44,
    61,
    77,
    87,
    122
   ],
   [
    7,
    15,
    20,
    67,
    78,
    95
   ],
   [
    8,
    16,
    53,
    68,
    79,
    122
   ],
   [
    9,
    17,
    54,
    69,
    80,
    123
   ],
   [
    10,
    18,
    48,
    65,
    81,
    119
   ],
   [
    11,
    19,
    49,
    66,
    82,
    120
   ],
   [
    20,
    50,
    62,
    83,
    93,
    121
   ],
   [
    0,
    12,
    21,
    66,
    84,
    101
   ],
   [
    13,
    22,
    51,
    73,
    85,
    121
   ],
   [
    14,
    23,
    52,
    74,
    86,
    96
   ],
   [
    15,
    24,
    29,
    73,
    87,
    104
   ],
   [
    4,
    16,
    25,
    74,
    75,
    88
   ],
   [
    17,
    26,
    59,
    76,
    89,
    125
   ],
   [
    1,
    18,
    27,
    69,
    70,
    90
   ],
   [
    19,
    28,
    56,
    71,
    91,
    124
   ],
   [
    20,
    29,
    57,
    72,
    92,
    102
   ],
   [
    2,
    21,
    30,
    71,
    93,
    110
   ],
   [
    3,
    22,
    31,
    72,
    81,
    94
   ],
   [
    23,
    32,
    58,
    82,
    95,
    105
   ],
   [
    24,
    33,
    38,
    81,
    96,
    113
   ],
   [
    10,
    25,
    34,
    82,
    84,
    97
   ],
   [
    11,
    26,
    35,
    83,
    85,
    98
   ],
   [
    5,
    27,
    36,
    76,
    78,
    99
   ],
   [
    6,
    28,
    37,
    77,
    79,
    100
   ],
   [
    29,
    38,
    61,
    80,
    101,
    111
   ],
   [
    7,
    30,
    39,
    79,
    102,
    118
   ],
   [
    8,
    31,
    40,
    80,
    90,
    103
   ],
   [
    9,
    32,
    41,
    63,
    91,
    104
   ],
   [
    33,
    42,
    47,
    90,
    105,
    120
   ],
   [
    18,
    34,
    43,
    91,
    93,
    106
   ],
   [
    19,
    35,
    44,
    92,
    94,
    107
   ],
   [
    12,
    36,
    45,
    85,
    87,
    108
   ],
   [
    13,
    37,
    46,
    86,
    88,
    109
   ],
   [
    14,
    38,
    47,
    64,
    89,
    110
   ],
   [
    15,
    39,
    48,
    88,
    111,
    123
   ],
   [
    16,
    40,
    49,
    89,
    99,
    112
   ],
   [
    17,
    41,
    50,
    65,
    100,
    113
   ],
   [
    27,
    43,
    51,
    100,
    102,
    114
   ],
   [
    28,
    44,
    52,
    101,
    103,
    115
   ],
   [
    21,
    45,
    53,
    94,
    96,
    116
   ],
   [
    22,
    46,
    54,
    95,
    97,
    117
   ],
   [
    23,
    47,
    55,
    68,
    98,
    118
   ],
   [
    25,
    49,
    56,
    98,
    108,
    119
   ],
   [
    26,
    50,
    57,
    70,
    109,
    120
   ],
   [
    37,
    52,
    58,
    110,
    112,
    121
   ],
   [
    31,
    54,
    59,
    104,
    106,
    122
   ],
   [
    32,
    55,
    60,
    75,
    107,
    123
   ],
   [
    35,
    57,
    61,
    78,
    117,
    124
   ],
   [
    41,
    60,
    62,
    84,
    115,
    125
   ]
  ],
  "Z": [
   [
    0,
    10,
    41,
    63,
    65,
    84
   ],
   [
    1,
    8,
    47,
    64,
    68,
    90
   ],
   [
    2,
    18,
    50,
    65,
    70,
    93
   ],
   [
    3,
    19,
    21,
    66,
    71,
    94
   ],
   [
    4,
    13,
    15,
    67,
    73,
    88
   ],
   [
    5,
    16,
    55,
    68,
    75,
    99
   ],
   [
    6,
    17,
    27,
    69,
    76,
    100
   ],
   [
    7,
    27,
    57,
    70,
    78,
    102
   ],
   [
    8,
    28,
    30,
    71,
    79,
    103
   ],
   [
    9,
    29,
    31,
    72,
    80,
    104
   ],
   [
    10,
    22,
    24,
    73,
    81,
    97
   ],
   [
    11,
    23,
    25,
    74,
    82,
    98
   ],
   [
    12,
    25,
    60,
    75,
    84,
    108
   ],
   [
    13,
    26,
    36,
    76,
    85,
    109
   ],
   [
    2,
    14,
    37,
    77,
    86,
    110
   ],
   [
    15,
    36,
    61,
    78,
    87,
    111
   ],
   [
    16,
    37,
    39,
    79,
    88,
    112
   ],
   [
    17,
    38,
    40,
    80,
    89,
    113
   ],
   [
    18,
    31,
    33,
    81,
    90,
    106
   ],
   [
    19,
    32,
    34,
    82,
    91,
    107
   ],
   [
    5,
    20,
    35,
    78,
    83,
    92
   ],
   [
    21,
    34,
    62,
    84,
    93,
    116
   ],
   [
    22,
    35,
    45,
    85,
    94,
    117
   ],
   [
    7,
    23,
    46,
    86,
    95,
    118
   ],
   [
    14,
    24,
    45,
    64,
    87,
    96
   ],
   [
    25,
    46,
    48,
    88,
    97,
    119
   ],
   [
    26,
    47,
    49,
    89,
    98,
    120
   ],
   [
    27,
    40,
    42,
    90,
    99,
    114
   ],
   [
    28,
    41,
    43,
    91,
    100,
    115
   ],
   [
    12,
    29,
    44,
    87,
    92,
    101
   ],
   [
    20,
    30,
    43,
    67,
    93,
    102
   ],
   [
    31,
    44,
    53,
    94,
    103,
    122
   ],
   [
    15,
    32,
    54,
    95,
    104,
    123
   ],
   [
    23,
    33,
    53,
    68,
    96,
    105
   ],
   [
    1,
    34,
    54,
    69,
    97,
    106
   ],
   [
    35,
    55,
    56,
    98,
    107,
    124
   ],
   [
    0,
    36,
    49,
    66,
    99,
    108
   ],
   [
    37,
    50,
    51,
    100,
    109,
    121
   ],
   [
    21,
    38,
    52,
    96,
    101,
    110
   ],
   [
    29,
    39,
    51,
    73,
    102,
    111
   ],
   [
    4,
    40,
    52,
    74,
    103,
    112
   ],
   [
    24,
    41,
    59,
    104,
    113,
    125
   ],
   [
    4,
    32,
    42,
    63,
    75,
    105
   ],
   [
    5,
    43,
    59,
    76,
    106,
    114
   ],
   [
    6,
    44,
    60,
    77,
    107,
    115
   ],
   [
    2,
    45,
    56,
    71,
    108,
    116
   ],
   [
    3,
    46,
    57,
    72,
    109,
    117
   ],
   [
    30,
    47,
    58,
    105,
    110,
    118
   ],
   [
    3,
    38,
    48,
    64,
    81,
    111
   ],
   [
    10,
    49,
    58,
    82,
    112,
    119
   ],
   [
    11,
    33,
    50,
    83,
    113,
    120
   ],
   [
    11,
    12,
    51,
    66,
    85,
    114
   ],
   [
    13,
    52,
    62,
    86,
    115,
    121
   ],
   [
    6,
    7,
    53,
    67,
    79,
    116
   ],
   [
    8,
    54,
    61,
    80,
    117,
    122
   ],
   [
    9,
    39,
    55,
    63,
    118,
    123
   ],
   [
    9,
    18,
    56,
    69,
    91,
    119
   ],
   [
    19,
    42,
    57,
    92,
    120,
    124
   ],
   [
    20,
    22,
    58,
    72,
    95,
    121
   ],
   [
    14,
    16,
    59,
    74,
    89,
    122
   ],
   [
    17,
    48,
    60,
    65,
    123,
    125
   ],
   [
    0,
    28,
    61,
    77,
    101,
    124
   ],
   [
    1,
    26,
    62,
    70,
    83,
    125
   ]
  ]
 },
 "distance": {
  "d": 14,
  "X": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    4,
    18,
    21,
    33,
    50,
    52,
    58,
    71,
    79,
    88,
    105,
    116,
    119,
    121
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1033
    ]
   }
  },
  "Z": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    1,
    5,
    9,
    23,
    27,
    32,
    48,
    81,
    92,
    94,
    96,
    102,
    118,
    123
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1034
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C63 = SmallGroup(63, 2) (order 63), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 126; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 2, 21}, b = {0, 10, 41} 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": "generalized-bicycle",
 "locality": {
  "coordinates": [
   [
    0.0,
    3.0
   ],
   [
    5.0,
    5.0
   ],
   [
    1.0,
    7.0
   ],
   [
    4.0,
    3.0
   ],
   [
    6.0,
    1.0
   ],
   [
    2.0,
    2.0
   ],
   [
    0.0,
    7.0
   ],
   [
    2.0,
    2.0
   ],
   [
    5.0,
    7.0
   ],
   [
    7.0,
    4.0
   ],
   [
    5.0,
    3.0
   ],
   [
    3.0,
    2.0
   ],
   [
    0.0,
    1.0
   ],
   [
    3.0,
    3.0
   ],
   [
    6.0,
    7.0
   ],
   [
    5.0,
    1.0
   ],
   [
    7.0,
    3.0
   ],
   [
    3.0,
    7.0
   ],
   [
    4.0,
    7.0
   ],
   [
    0.0,
    2.0
   ],
   [
    2.0,
    1.0
   ],
   [
    1.0,
    6.0
   ],
   [
    5.0,
    4.0
   ],
   [
    7.0,
    2.0
   ],
   [
    7.0,
    6.0
   ],
   [
    3.0,
    1.0
   ],
   [
    1.0,
    2.0
   ],
   [
    1.0,
    3.0
   ],
   [
    0.0,
    7.0
   ],
   [
    2.0,
    5.0
   ],
   [
    3.0,
    4.0
   ],
   [
    7.0,
    7.0
   ],
   [
    5.0,
    2.0
   ],
   [
    6.0,
    3.0
   ],
   [
    3.0,
    6.0
   ],
   [
    1.0,
    1.0
   ],
   [
    0.0,
    0.0
   ],
   [
    4.0,
    4.0
   ],
   [
    6.0,
    7.0
   ],
   [
    5.0,
    1.0
   ],
   [
    6.0,
    4.0
   ],
   [
    3.0,
    6.0
   ],
   [
    4.0,
    0.0
   ],
   [
    0.0,
    4.0
   ],
   [
    2.0,
    6.0
   ],
   [
    2.0,
    5.0
   ],
   [
    7.0,
    0.0
   ],
   [
    6.0,
    2.0
   ],
   [
    6.0,
    5.0
   ],
   [
    3.0,
    0.0
   ],
   [
    1.0,
    5.0
   ],
   [
    2.0,
    0.0
   ],
   [
    4.0,
    5.0
   ],
   [
    5.0,
    6.0
   ],
   [
    7.0,
    5.0
   ],
   [
    5.0,
    0.0
   ],
   [
    3.0,
    5.0
   ],
   [
    2.0,
    0.0
   ],
   [
    6.0,
    1.0
   ],
   [
    4.0,
    6.0
   ],
   [
    1.0,
    4.0
   ],
   [
    2.0,
    4.0
   ],
   [
    0.0,
    5.0
   ],
   [
    4.0,
    2.0
   ],
   [
    7.0,
    6.0
   ],
   [
    2.0,
    7.0
   ],
   [
    0.0,
    2.0
   ],
   [
    3.0,
    3.0
   ],
   [
    7.0,
    3.0
   ],
   [
    4.0,
    7.0
   ],
   [
    2.0,
    3.0
   ],
   [
    2.0,
    7.0
   ],
   [
    5.0,
    2.0
   ],
   [
    6.0,
    2.0
   ],
   [
    7.0,
    4.0
   ],
   [
    4.0,
    0.0
   ],
   [
    1.0,
    3.0
   ],
   [
    1.0,
    7.0
   ],
   [
    1.0,
    0.0
   ],
   [
    4.0,
    4.0
   ],
   [
    6.0,
    6.0
   ],
   [
    7.0,
    7.0
   ],
   [
    4.0,
    1.0
   ],
   [
    2.0,
    3.0
   ],
   [
    1.0,
    5.0
   ],
   [
    1.0,
    1.0
   ],
   [
    5.0,
    5.0
   ],
   [
    2.0,
    4.0
   ],
   [
    7.0,
    1.0
   ],
   [
    5.0,
    4.0
   ],
   [
    6.0,
    3.0
   ],
   [
    3.0,
    5.0
   ],
   [
    0.0,
    1.0
   ],
   [
    0.0,
    5.0
   ],
   [
    2.0,
    6.0
   ],
   [
    6.0,
    0.0
   ],
   [
    5.0,
    7.0
   ],
   [
    6.0,
    5.0
   ],
   [
    5.0,
    0.0
   ],
   [
    3.0,
    1.0
   ],
   [
    0.0,
    4.0
   ],
   [
    1.0,
    6.0
   ],
   [
    1.0,
    0.0
   ],
   [
    4.0,
    5.0
   ],
   [
    7.0,
    5.0
   ],
   [
    7.0,
    2.0
   ],
   [
    4.0,
    6.0
   ],
   [
    1.0,
    4.0
   ],
   [
    1.0,
    2.0
   ],
   [
    3.0,
    0.0
   ],
   [
    3.0,
    4.0
   ],
   [
    4.0,
    3.0
   ],
   [
    7.0,
    1.0
   ],
   [
    5.0,
    6.0
   ],
   [
    3.0,
    2.0
   ],
   [
    0.0,
    6.0
   ],
   [
    0.0,
    6.0
   ],
   [
    4.0,
    2.0
   ],
   [
    6.0,
    0.0
   ],
   [
    6.0,
    4.0
   ],
   [
    4.0,
    1.0
   ],
   [
    2.0,
    1.0
   ],
   [
    6.0,
    6.0
   ],
   [
    5.0,
    3.0
   ],
   [
    0.0,
    3.0
   ],
   [
    3.0,
    7.0
   ]
  ],
  "layers": 2,
  "interaction_radius": 5.831,
  "contributed_by": {
   "by": [
    "@MathysRennela"
   ],
   "date": "2026-10-13",
   "method": "Simulated annealing over integer-grid site assignments with the repo's own research/local2d/fold_layout.search_layout, single layer at radius 4 then two layers at 7, plus a divisor scan of the two-block index convention Z_l x Z_m which gives the tighter embedding here; radius and per-site occupancy re-measured with the verifier's own rule."
  }
 }
}