{
 "schema_version": "0.1",
 "name": "[[150,24,13]] two-block code over C15 x C5 (Lee, arXiv:2610.13880)",
 "code_type": "CSS",
 "n": 150,
 "k": 24,
 "checks": {
  "X": [
   [
    0,
    21,
    30,
    45,
    63,
    75,
    101,
    114,
    147
   ],
   [
    1,
    9,
    27,
    39,
    68,
    76,
    110,
    123,
    139
   ],
   [
    2,
    18,
    33,
    43,
    56,
    75,
    77,
    127,
    149
   ],
   [
    0,
    3,
    34,
    57,
    70,
    76,
    78,
    106,
    115
   ],
   [
    4,
    14,
    36,
    48,
    71,
    79,
    105,
    119,
    144
   ],
   [
    5,
    17,
    25,
    40,
    52,
    76,
    80,
    134,
    145
   ],
   [
    1,
    6,
    18,
    41,
    73,
    79,
    81,
    90,
    124
   ],
   [
    7,
    11,
    29,
    46,
    55,
    77,
    82,
    123,
    137
   ],
   [
    2,
    8,
    30,
    47,
    65,
    78,
    80,
    83,
    119
   ],
   [
    3,
    9,
    26,
    48,
    66,
    81,
    84,
    120,
    128
   ],
   [
    10,
    24,
    34,
    49,
    59,
    79,
    85,
    118,
    148
   ],
   [
    4,
    11,
    25,
    50,
    74,
    75,
    86,
    97,
    131
   ],
   [
    3,
    12,
    28,
    38,
    62,
    80,
    87,
    105,
    142
   ],
   [
    5,
    13,
    29,
    39,
    53,
    81,
    85,
    88,
    101
   ],
   [
    6,
    14,
    30,
    35,
    54,
    86,
    89,
    102,
    135
   ],
   [
    15,
    20,
    42,
    57,
    64,
    82,
    90,
    134,
    144
   ],
   [
    7,
    16,
    21,
    43,
    58,
    79,
    83,
    87,
    91
   ],
   [
    0,
    8,
    17,
    59,
    71,
    84,
    88,
    92,
    131
   ],
   [
    4,
    9,
    18,
    40,
    72,
    89,
    93,
    132,
    138
   ],
   [
    6,
    19,
    37,
    47,
    67,
    85,
    94,
    114,
    130
   ],
   [
    10,
    20,
    38,
    48,
    60,
    77,
    86,
    95,
    110
   ],
   [
    11,
    21,
    39,
    44,
    61,
    78,
    96,
    111,
    140
   ],
   [
    8,
    22,
    41,
    51,
    69,
    87,
    97,
    118,
    147
   ],
   [
    9,
    12,
    23,
    42,
    52,
    75,
    88,
    94,
    98
   ],
   [
    1,
    13,
    24,
    43,
    63,
    89,
    95,
    99,
    115
   ],
   [
    0,
    14,
    25,
    49,
    64,
    96,
    100,
    116,
    143
   ],
   [
    26,
    32,
    54,
    65,
    70,
    90,
    101,
    142,
    148
   ],
   [
    15,
    27,
    33,
    55,
    66,
    85,
    91,
    97,
    102
   ],
   [
    2,
    16,
    28,
    34,
    67,
    86,
    92,
    98,
    103
   ],
   [
    3,
    10,
    17,
    29,
    74,
    93,
    99,
    104,
    140
   ],
   [
    11,
    18,
    30,
    31,
    53,
    100,
    105,
    141,
    145
   ],
   [
    13,
    31,
    50,
    58,
    72,
    94,
    106,
    127,
    139
   ],
   [
    14,
    19,
    32,
    51,
    59,
    76,
    82,
    95,
    107
   ],
   [
    4,
    20,
    33,
    52,
    68,
    83,
    96,
    108,
    124
   ],
   [
    1,
    21,
    34,
    56,
    69,
    84,
    109,
    125,
    146
   ],
   [
    16,
    35,
    53,
    61,
    73,
    97,
    110,
    130,
    149
   ],
   [
    17,
    22,
    36,
    54,
    62,
    77,
    98,
    106,
    111
   ],
   [
    5,
    18,
    23,
    37,
    55,
    78,
    99,
    107,
    112
   ],
   [
    2,
    6,
    24,
    38,
    70,
    100,
    108,
    113,
    128
   ],
   [
    3,
    15,
    25,
    39,
    60,
    109,
    114,
    129,
    148
   ],
   [
    26,
    40,
    46,
    64,
    71,
    94,
    102,
    110,
    115
   ],
   [
    7,
    27,
    41,
    47,
    72,
    95,
    103,
    111,
    116
   ],
   [
    8,
    19,
    28,
    42,
    48,
    96,
    104,
    112,
    117
   ],
   [
    9,
    20,
    29,
    43,
    44,
    105,
    113,
    118,
    146
   ],
   [
    23,
    44,
    60,
    66,
    74,
    106,
    119,
    137,
    145
   ],
   [
    24,
    31,
    45,
    61,
    67,
    80,
    90,
    107,
    120
   ],
   [
    10,
    25,
    32,
    46,
    62,
    81,
    91,
    108,
    121
   ],
   [
    5,
    11,
    33,
    47,
    73,
    92,
    109,
    122,
    135
   ],
   [
    6,
    22,
    34,
    48,
    65,
    93,
    123,
    136,
    149
   ],
   [
    28,
    35,
    49,
    63,
    69,
    82,
    111,
    119,
    124
   ],
   [
    12,
    29,
    36,
    50,
    64,
    83,
    112,
    120,
    125
   ],
   [
    7,
    13,
    30,
    37,
    51,
    84,
    113,
    121,
    126
   ],
   [
    8,
    14,
    26,
    38,
    52,
    114,
    122,
    127,
    138
   ],
   [
    15,
    40,
    53,
    58,
    74,
    107,
    116,
    124,
    128
   ],
   [
    16,
    31,
    41,
    54,
    59,
    108,
    117,
    125,
    129
   ],
   [
    4,
    17,
    32,
    42,
    55,
    109,
    118,
    126,
    130
   ],
   [
    37,
    44,
    56,
    68,
    72,
    87,
    101,
    120,
    131
   ],
   [
    19,
    38,
    45,
    57,
    69,
    88,
    102,
    121,
    132
   ],
   [
    12,
    20,
    39,
    46,
    58,
    89,
    103,
    122,
    133
   ],
   [
    13,
    21,
    35,
    47,
    59,
    104,
    123,
    134,
    143
   ],
   [
    22,
    42,
    49,
    60,
    70,
    91,
    125,
    131,
    135
   ],
   [
    15,
    23,
    43,
    50,
    61,
    92,
    126,
    132,
    136
   ],
   [
    0,
    16,
    24,
    51,
    62,
    93,
    127,
    133,
    137
   ],
   [
    27,
    44,
    53,
    63,
    67,
    121,
    129,
    135,
    138
   ],
   [
    10,
    28,
    45,
    54,
    64,
    122,
    130,
    136,
    139
   ],
   [
    31,
    51,
    56,
    65,
    73,
    98,
    115,
    132,
    140
   ],
   [
    22,
    32,
    52,
    57,
    66,
    99,
    116,
    133,
    141
   ],
   [
    1,
    23,
    33,
    58,
    67,
    100,
    117,
    134,
    142
   ],
   [
    26,
    36,
    55,
    60,
    68,
    103,
    136,
    140,
    143
   ],
   [
    2,
    27,
    37,
    61,
    69,
    104,
    137,
    141,
    144
   ],
   [
    19,
    41,
    56,
    63,
    70,
    133,
    139,
    143,
    145
   ],
   [
    35,
    45,
    62,
    65,
    71,
    112,
    128,
    141,
    146
   ],
   [
    5,
    36,
    46,
    66,
    72,
    113,
    129,
    142,
    147
   ],
   [
    7,
    40,
    50,
    68,
    73,
    117,
    144,
    146,
    148
   ],
   [
    12,
    49,
    57,
    71,
    74,
    126,
    138,
    147,
    149
   ]
  ],
  "Z": [
   [
    0,
    2,
    11,
    23,
    75,
    78,
    92,
    100,
    137
   ],
   [
    1,
    3,
    5,
    32,
    76,
    81,
    99,
    109,
    142
   ],
   [
    2,
    7,
    20,
    36,
    77,
    83,
    103,
    113,
    144
   ],
   [
    3,
    8,
    21,
    37,
    78,
    84,
    87,
    104,
    114
   ],
   [
    4,
    6,
    10,
    16,
    79,
    86,
    93,
    108,
    130
   ],
   [
    5,
    8,
    12,
    45,
    80,
    88,
    112,
    122,
    147
   ],
   [
    6,
    9,
    13,
    46,
    81,
    89,
    94,
    113,
    123
   ],
   [
    7,
    15,
    32,
    49,
    82,
    91,
    116,
    126,
    148
   ],
   [
    8,
    16,
    33,
    50,
    83,
    92,
    97,
    117,
    127
   ],
   [
    9,
    17,
    34,
    51,
    76,
    84,
    93,
    98,
    118
   ],
   [
    10,
    13,
    19,
    27,
    85,
    95,
    104,
    121,
    139
   ],
   [
    11,
    14,
    20,
    28,
    82,
    86,
    96,
    105,
    122
   ],
   [
    12,
    16,
    22,
    56,
    87,
    98,
    125,
    133,
    149
   ],
   [
    13,
    17,
    23,
    57,
    88,
    99,
    106,
    126,
    134
   ],
   [
    14,
    18,
    24,
    58,
    79,
    89,
    100,
    107,
    127
   ],
   [
    6,
    15,
    26,
    45,
    90,
    102,
    114,
    128,
    136
   ],
   [
    16,
    27,
    46,
    60,
    91,
    103,
    110,
    129,
    137
   ],
   [
    17,
    28,
    47,
    61,
    80,
    92,
    104,
    111,
    130
   ],
   [
    18,
    29,
    48,
    62,
    77,
    81,
    93,
    105,
    112
   ],
   [
    19,
    23,
    31,
    40,
    94,
    107,
    117,
    132,
    145
   ],
   [
    20,
    24,
    32,
    41,
    90,
    95,
    108,
    118,
    133
   ],
   [
    21,
    25,
    33,
    42,
    75,
    91,
    96,
    109,
    134
   ],
   [
    11,
    22,
    27,
    35,
    97,
    111,
    123,
    135,
    141
   ],
   [
    23,
    28,
    36,
    65,
    98,
    112,
    119,
    136,
    142
   ],
   [
    24,
    29,
    37,
    66,
    85,
    99,
    113,
    120,
    137
   ],
   [
    25,
    30,
    38,
    67,
    80,
    86,
    100,
    114,
    121
   ],
   [
    0,
    13,
    26,
    56,
    84,
    101,
    115,
    127,
    143
   ],
   [
    14,
    27,
    40,
    57,
    76,
    102,
    116,
    138,
    144
   ],
   [
    28,
    41,
    58,
    68,
    87,
    103,
    117,
    124,
    139
   ],
   [
    29,
    42,
    59,
    69,
    82,
    88,
    104,
    118,
    125
   ],
   [
    4,
    12,
    30,
    43,
    75,
    83,
    89,
    105,
    126
   ],
   [
    3,
    31,
    36,
    44,
    105,
    106,
    120,
    129,
    140
   ],
   [
    32,
    37,
    45,
    53,
    101,
    107,
    121,
    130,
    141
   ],
   [
    33,
    38,
    46,
    54,
    77,
    102,
    108,
    122,
    142
   ],
   [
    34,
    39,
    47,
    55,
    78,
    85,
    103,
    109,
    123
   ],
   [
    1,
    20,
    35,
    40,
    89,
    110,
    124,
    134,
    146
   ],
   [
    21,
    36,
    41,
    49,
    79,
    111,
    125,
    143,
    147
   ],
   [
    37,
    42,
    50,
    71,
    94,
    112,
    126,
    131,
    144
   ],
   [
    38,
    43,
    51,
    72,
    87,
    95,
    113,
    127,
    132
   ],
   [
    0,
    19,
    39,
    52,
    76,
    88,
    96,
    114,
    133
   ],
   [
    3,
    24,
    40,
    65,
    80,
    93,
    115,
    128,
    148
   ],
   [
    25,
    41,
    53,
    66,
    81,
    97,
    116,
    129,
    145
   ],
   [
    42,
    54,
    67,
    73,
    90,
    98,
    117,
    130,
    135
   ],
   [
    10,
    22,
    43,
    55,
    77,
    91,
    99,
    118,
    136
   ],
   [
    4,
    8,
    44,
    49,
    96,
    118,
    119,
    131,
    138
   ],
   [
    9,
    45,
    50,
    56,
    75,
    120,
    132,
    139,
    146
   ],
   [
    46,
    51,
    57,
    63,
    82,
    115,
    121,
    133,
    147
   ],
   [
    47,
    52,
    58,
    64,
    83,
    94,
    116,
    122,
    134
   ],
   [
    1,
    7,
    48,
    59,
    79,
    84,
    95,
    117,
    123
   ],
   [
    6,
    33,
    49,
    53,
    85,
    100,
    124,
    135,
    149
   ],
   [
    34,
    50,
    54,
    60,
    86,
    106,
    125,
    136,
    148
   ],
   [
    51,
    55,
    61,
    74,
    97,
    107,
    126,
    137,
    140
   ],
   [
    2,
    31,
    52,
    62,
    80,
    98,
    108,
    127,
    141
   ],
   [
    9,
    38,
    53,
    71,
    88,
    105,
    110,
    128,
    138
   ],
   [
    39,
    54,
    63,
    72,
    89,
    101,
    111,
    129,
    139
   ],
   [
    19,
    35,
    55,
    64,
    82,
    102,
    112,
    130,
    143
   ],
   [
    11,
    17,
    56,
    60,
    77,
    109,
    131,
    140,
    145
   ],
   [
    18,
    57,
    61,
    65,
    78,
    90,
    132,
    141,
    149
   ],
   [
    58,
    62,
    66,
    70,
    91,
    106,
    128,
    133,
    142
   ],
   [
    5,
    15,
    59,
    67,
    85,
    92,
    107,
    129,
    134
   ],
   [
    14,
    47,
    60,
    63,
    95,
    114,
    119,
    135,
    143
   ],
   [
    48,
    61,
    64,
    68,
    96,
    110,
    120,
    136,
    144
   ],
   [
    7,
    44,
    62,
    69,
    87,
    111,
    121,
    137,
    146
   ],
   [
    18,
    52,
    63,
    74,
    75,
    99,
    124,
    138,
    145
   ],
   [
    1,
    31,
    64,
    70,
    90,
    100,
    115,
    125,
    139
   ],
   [
    21,
    29,
    65,
    68,
    83,
    101,
    123,
    140,
    146
   ],
   [
    30,
    66,
    69,
    71,
    84,
    102,
    119,
    141,
    147
   ],
   [
    12,
    26,
    67,
    72,
    94,
    103,
    120,
    138,
    142
   ],
   [
    25,
    59,
    68,
    70,
    76,
    108,
    131,
    143,
    148
   ],
   [
    4,
    15,
    69,
    73,
    97,
    109,
    124,
    132,
    144
   ],
   [
    5,
    30,
    44,
    70,
    78,
    101,
    113,
    135,
    145
   ],
   [
    34,
    43,
    71,
    73,
    79,
    92,
    115,
    146,
    149
   ],
   [
    0,
    22,
    72,
    74,
    93,
    106,
    116,
    131,
    147
   ],
   [
    10,
    26,
    39,
    73,
    81,
    110,
    122,
    140,
    148
   ],
   [
    2,
    35,
    48,
    74,
    86,
    104,
    119,
    128,
    149
   ]
  ]
 },
 "distance": {
  "d": 13,
  "X": {
   "value": 13,
   "confidence": "upper_bound",
   "witness": [
    3,
    21,
    23,
    43,
    65,
    75,
    92,
    97,
    99,
    111,
    129,
    132,
    137
   ]
  },
  "Z": {
   "value": 13,
   "confidence": "upper_bound",
   "witness": [
    4,
    27,
    36,
    37,
    46,
    50,
    55,
    68,
    94,
    98,
    103,
    121,
    132
   ]
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) of arXiv:2610.13880 (Tables 2 and 11) over the abelian group C15 x C5 (GAP SmallGroup(75,3)): H_X = (L(a) | R(b)), H_Z = (R(b)^T | L(a)^T) with L and R the left and right regular representations, a = 1 + y + x^6 y^2 + x^7 y^4 + x^10 y^3, b = 1 + x^5 y + x^6 + x^7 y in generators x (order 15) and y (order 5), i.e. the bivariate bicycle code with A = a(x,y), B = b(x,y). The stored matrices use the qubit ordering of the paper's database (record dcad62c28a19ac97, github.com/gideonlsx/bicycle-race @ aed705a, data/codes.jsonl, CC BY 4.0): qubits 0..74 are the left block and 75..149 the right block, group elements numbered as GAP's Elements(SmallGroup(75,3)) with e0 the identity, x = e5, y = e3, so a = e0 + e3 + e17 + e25 + e62, b = e0 + e2 + e11 + e23. Rebuilt from the database's group data; CSS commutation, k, check weight and both of the paper's witnesses were re-checked on the rebuilt matrices.",
  "origin": "baseline",
  "date": "2026-10-12",
  "model": "Claude Fable 5.1 (Claude Code)",
  "notes": "Literature reconstruction. The paper states d = 13 exactly (d_X: equal to d_Z by a checked X/Z-exchange automorphism; d_Z: ladder (cluster engine, symmetry roots), from the screen's lower bound 12, no target; verification record: verified: second exact engine (dist-m4ri from symmetry roots), GAP rebuild, QDistRnd, QDistEvol). Readings here: qldpc submit's RIS (20,000 NumPy trials per side) and its 2,000,000-trial accelerator pass, plus the verifier's refutation search; witnessed upper bound, see notes/150-24-13.md.",
  "novelty": "known_parameters",
  "references": [
   "arXiv:2610.13880"
  ]
 },
 "family": "bivariate-bicycle"
}
