{
 "schema_version": "0.3",
 "name": "Same124-20-13 group, weight13 degree12 generator basis",
 "code_type": "CSS",
 "n": 124,
 "k": 20,
 "checks": {
  "X": [
   [
    0,
    40,
    46,
    47,
    57,
    60,
    61,
    62,
    98,
    100,
    101,
    117,
    123
   ],
   [
    1,
    41,
    46,
    56,
    57,
    60,
    63,
    99,
    100,
    116,
    117,
    122,
    123
   ],
   [
    0,
    3,
    43,
    48,
    58,
    59,
    62,
    63,
    65,
    101,
    102,
    118,
    119
   ],
   [
    2,
    5,
    45,
    50,
    60,
    61,
    64,
    65,
    67,
    103,
    104,
    120,
    121
   ],
   [
    1,
    4,
    5,
    6,
    46,
    52,
    53,
    67,
    68,
    104,
    106,
    107,
    123
   ],
   [
    0,
    1,
    4,
    7,
    47,
    52,
    66,
    67,
    69,
    105,
    106,
    122,
    123
   ],
   [
    3,
    6,
    7,
    8,
    48,
    54,
    55,
    63,
    69,
    70,
    106,
    108,
    109
   ],
   [
    2,
    3,
    6,
    9,
    49,
    54,
    62,
    63,
    68,
    69,
    71,
    107,
    108
   ],
   [
    5,
    8,
    9,
    10,
    50,
    56,
    57,
    65,
    71,
    72,
    108,
    110,
    111
   ],
   [
    4,
    5,
    8,
    11,
    51,
    56,
    64,
    65,
    70,
    71,
    73,
    109,
    110
   ],
   [
    7,
    10,
    11,
    12,
    52,
    58,
    59,
    67,
    73,
    74,
    110,
    112,
    113
   ],
   [
    6,
    7,
    10,
    13,
    53,
    58,
    66,
    67,
    72,
    73,
    75,
    111,
    112
   ],
   [
    9,
    12,
    13,
    14,
    54,
    60,
    61,
    69,
    75,
    76,
    112,
    114,
    115
   ],
   [
    8,
    9,
    12,
    15,
    55,
    60,
    68,
    69,
    74,
    75,
    77,
    113,
    114
   ],
   [
    0,
    1,
    11,
    14,
    15,
    16,
    56,
    71,
    77,
    78,
    114,
    116,
    117
   ],
   [
    0,
    10,
    11,
    14,
    17,
    57,
    70,
    71,
    76,
    77,
    79,
    115,
    116
   ],
   [
    2,
    3,
    13,
    16,
    17,
    18,
    58,
    73,
    79,
    80,
    116,
    118,
    119
   ],
   [
    2,
    12,
    13,
    16,
    19,
    59,
    72,
    73,
    78,
    79,
    81,
    117,
    118
   ],
   [
    4,
    5,
    15,
    18,
    19,
    20,
    60,
    75,
    81,
    82,
    118,
    120,
    121
   ],
   [
    4,
    14,
    15,
    18,
    21,
    61,
    74,
    75,
    80,
    81,
    83,
    119,
    120
   ],
   [
    0,
    6,
    7,
    17,
    20,
    21,
    22,
    77,
    83,
    84,
    120,
    122,
    123
   ],
   [
    1,
    6,
    16,
    17,
    20,
    23,
    76,
    77,
    82,
    83,
    85,
    121,
    122
   ],
   [
    2,
    8,
    9,
    19,
    22,
    23,
    24,
    62,
    63,
    79,
    85,
    86,
    122
   ],
   [
    3,
    8,
    18,
    19,
    22,
    25,
    62,
    78,
    79,
    84,
    85,
    87,
    123
   ],
   [
    4,
    10,
    11,
    21,
    24,
    25,
    26,
    62,
    64,
    65,
    81,
    87,
    88
   ],
   [
    5,
    10,
    20,
    21,
    24,
    27,
    63,
    64,
    80,
    81,
    86,
    87,
    89
   ],
   [
    6,
    12,
    13,
    23,
    26,
    27,
    28,
    64,
    66,
    67,
    83,
    89,
    90
   ],
   [
    7,
    12,
    22,
    23,
    26,
    29,
    65,
    66,
    82,
    83,
    88,
    89,
    91
   ],
   [
    8,
    14,
    15,
    25,
    28,
    29,
    30,
    66,
    68,
    69,
    85,
    91,
    92
   ],
   [
    9,
    14,
    24,
    25,
    28,
    31,
    67,
    68,
    84,
    85,
    90,
    91,
    93
   ],
   [
    10,
    16,
    17,
    27,
    30,
    31,
    32,
    68,
    70,
    71,
    87,
    93,
    94
   ],
   [
    11,
    16,
    26,
    27,
    30,
    33,
    69,
    70,
    86,
    87,
    92,
    93,
    95
   ],
   [
    13,
    18,
    28,
    29,
    32,
    35,
    71,
    72,
    88,
    89,
    94,
    95,
    97
   ],
   [
    14,
    20,
    21,
    31,
    34,
    35,
    36,
    72,
    74,
    75,
    91,
    97,
    98
   ],
   [
    15,
    20,
    30,
    31,
    34,
    37,
    73,
    74,
    90,
    91,
    96,
    97,
    99
   ],
   [
    16,
    22,
    23,
    33,
    36,
    37,
    38,
    74,
    76,
    77,
    93,
    99,
    100
   ],
   [
    17,
    22,
    32,
    33,
    36,
    39,
    75,
    76,
    92,
    93,
    98,
    99,
    101
   ],
   [
    18,
    24,
    25,
    35,
    38,
    39,
    40,
    76,
    78,
    79,
    95,
    101,
    102
   ],
   [
    19,
    24,
    34,
    35,
    38,
    41,
    77,
    78,
    94,
    95,
    100,
    101,
    103
   ],
   [
    20,
    26,
    27,
    37,
    40,
    41,
    42,
    78,
    80,
    81,
    97,
    103,
    104
   ],
   [
    21,
    26,
    36,
    37,
    40,
    43,
    79,
    80,
    96,
    97,
    102,
    103,
    105
   ],
   [
    23,
    28,
    38,
    39,
    42,
    45,
    81,
    82,
    98,
    99,
    104,
    105,
    107
   ],
   [
    25,
    30,
    40,
    41,
    44,
    47,
    83,
    84,
    100,
    101,
    106,
    107,
    109
   ],
   [
    26,
    32,
    33,
    43,
    46,
    47,
    48,
    84,
    86,
    87,
    103,
    109,
    110
   ],
   [
    27,
    32,
    42,
    43,
    46,
    49,
    85,
    86,
    102,
    103,
    108,
    109,
    111
   ],
   [
    28,
    34,
    35,
    45,
    48,
    49,
    50,
    86,
    88,
    89,
    105,
    111,
    112
   ],
   [
    29,
    34,
    44,
    45,
    48,
    51,
    87,
    88,
    104,
    105,
    110,
    111,
    113
   ],
   [
    30,
    36,
    37,
    47,
    50,
    51,
    52,
    88,
    90,
    91,
    107,
    113,
    114
   ],
   [
    32,
    38,
    39,
    49,
    52,
    53,
    54,
    90,
    92,
    93,
    109,
    115,
    116
   ],
   [
    34,
    40,
    41,
    51,
    54,
    55,
    56,
    92,
    94,
    95,
    111,
    117,
    118
   ],
   [
    36,
    42,
    43,
    53,
    56,
    57,
    58,
    94,
    96,
    97,
    113,
    119,
    120
   ],
   [
    38,
    44,
    45,
    55,
    58,
    59,
    60,
    96,
    98,
    99,
    115,
    121,
    122
   ]
  ],
  "Z": [
   [
    0,
    3,
    9,
    24,
    25,
    26,
    62,
    64,
    65,
    69,
    78,
    79,
    84
   ],
   [
    5,
    6,
    7,
    12,
    13,
    28,
    31,
    67,
    68,
    72,
    73,
    82,
    89
   ],
   [
    6,
    9,
    15,
    30,
    31,
    32,
    68,
    70,
    71,
    75,
    84,
    85,
    90
   ],
   [
    7,
    8,
    9,
    14,
    15,
    30,
    33,
    69,
    70,
    74,
    75,
    84,
    91
   ],
   [
    8,
    11,
    17,
    32,
    33,
    34,
    70,
    72,
    73,
    77,
    86,
    87,
    92
   ],
   [
    9,
    10,
    11,
    16,
    17,
    32,
    35,
    71,
    72,
    76,
    77,
    86,
    93
   ],
   [
    10,
    13,
    19,
    34,
    35,
    36,
    72,
    74,
    75,
    79,
    88,
    89,
    94
   ],
   [
    11,
    12,
    13,
    18,
    19,
    34,
    37,
    73,
    74,
    78,
    79,
    88,
    95
   ],
   [
    12,
    15,
    21,
    36,
    37,
    38,
    74,
    76,
    77,
    81,
    90,
    91,
    96
   ],
   [
    13,
    14,
    15,
    20,
    21,
    36,
    39,
    75,
    76,
    80,
    81,
    90,
    97
   ],
   [
    14,
    17,
    23,
    38,
    39,
    40,
    76,
    78,
    79,
    83,
    92,
    93,
    98
   ],
   [
    15,
    16,
    17,
    22,
    23,
    38,
    41,
    77,
    78,
    82,
    83,
    92,
    99
   ],
   [
    16,
    19,
    25,
    40,
    41,
    42,
    78,
    80,
    81,
    85,
    94,
    95,
    100
   ],
   [
    17,
    18,
    19,
    24,
    25,
    40,
    43,
    79,
    80,
    84,
    85,
    94,
    101
   ],
   [
    18,
    21,
    27,
    42,
    43,
    44,
    80,
    82,
    83,
    87,
    96,
    97,
    102
   ],
   [
    19,
    20,
    21,
    26,
    27,
    42,
    45,
    81,
    82,
    86,
    87,
    96,
    103
   ],
   [
    20,
    23,
    29,
    44,
    45,
    46,
    82,
    84,
    85,
    89,
    98,
    99,
    104
   ],
   [
    21,
    22,
    23,
    28,
    29,
    44,
    47,
    83,
    84,
    88,
    89,
    98,
    105
   ],
   [
    22,
    25,
    31,
    46,
    47,
    48,
    84,
    86,
    87,
    91,
    100,
    101,
    106
   ],
   [
    23,
    24,
    25,
    30,
    31,
    46,
    49,
    85,
    86,
    90,
    91,
    100,
    107
   ],
   [
    24,
    27,
    33,
    48,
    49,
    50,
    86,
    88,
    89,
    93,
    102,
    103,
    108
   ],
   [
    25,
    26,
    27,
    32,
    33,
    48,
    51,
    87,
    88,
    92,
    93,
    102,
    109
   ],
   [
    26,
    29,
    35,
    50,
    51,
    52,
    88,
    90,
    91,
    95,
    104,
    105,
    110
   ],
   [
    27,
    28,
    29,
    34,
    35,
    50,
    53,
    89,
    90,
    94,
    95,
    104,
    111
   ],
   [
    28,
    31,
    37,
    52,
    53,
    54,
    90,
    92,
    93,
    97,
    106,
    107,
    112
   ],
   [
    29,
    30,
    31,
    36,
    37,
    52,
    55,
    91,
    92,
    96,
    97,
    106,
    113
   ],
   [
    30,
    33,
    39,
    54,
    55,
    56,
    92,
    94,
    95,
    99,
    108,
    109,
    114
   ],
   [
    31,
    32,
    33,
    38,
    39,
    54,
    57,
    93,
    94,
    98,
    99,
    108,
    115
   ],
   [
    32,
    35,
    41,
    56,
    57,
    58,
    94,
    96,
    97,
    101,
    110,
    111,
    116
   ],
   [
    33,
    34,
    35,
    40,
    41,
    56,
    59,
    95,
    96,
    100,
    101,
    110,
    117
   ],
   [
    34,
    37,
    43,
    58,
    59,
    60,
    96,
    98,
    99,
    103,
    112,
    113,
    118
   ],
   [
    35,
    36,
    37,
    42,
    43,
    58,
    61,
    97,
    98,
    102,
    103,
    112,
    119
   ],
   [
    0,
    36,
    39,
    45,
    60,
    61,
    98,
    100,
    101,
    105,
    114,
    115,
    120
   ],
   [
    1,
    37,
    38,
    39,
    44,
    45,
    60,
    99,
    100,
    104,
    105,
    114,
    121
   ],
   [
    0,
    1,
    2,
    38,
    41,
    47,
    100,
    102,
    103,
    107,
    116,
    117,
    122
   ],
   [
    0,
    3,
    39,
    40,
    41,
    46,
    47,
    101,
    102,
    106,
    107,
    116,
    123
   ],
   [
    2,
    3,
    4,
    40,
    43,
    49,
    62,
    102,
    104,
    105,
    109,
    118,
    119
   ],
   [
    2,
    5,
    41,
    42,
    43,
    48,
    49,
    63,
    103,
    104,
    108,
    109,
    118
   ],
   [
    4,
    5,
    6,
    42,
    45,
    51,
    64,
    104,
    106,
    107,
    111,
    120,
    121
   ],
   [
    4,
    7,
    43,
    44,
    45,
    50,
    51,
    65,
    105,
    106,
    110,
    111,
    120
   ],
   [
    6,
    7,
    8,
    44,
    47,
    53,
    66,
    106,
    108,
    109,
    113,
    122,
    123
   ],
   [
    6,
    9,
    45,
    46,
    47,
    52,
    53,
    67,
    107,
    108,
    112,
    113,
    122
   ],
   [
    8,
    9,
    10,
    46,
    49,
    55,
    62,
    63,
    68,
    108,
    110,
    111,
    115
   ],
   [
    8,
    11,
    47,
    48,
    49,
    54,
    55,
    62,
    69,
    109,
    110,
    114,
    115
   ],
   [
    10,
    11,
    12,
    48,
    51,
    57,
    64,
    65,
    70,
    110,
    112,
    113,
    117
   ],
   [
    10,
    13,
    49,
    50,
    51,
    56,
    57,
    64,
    71,
    111,
    112,
    116,
    117
   ],
   [
    12,
    13,
    14,
    50,
    53,
    59,
    66,
    67,
    72,
    112,
    114,
    115,
    119
   ],
   [
    12,
    15,
    51,
    52,
    53,
    58,
    59,
    66,
    73,
    113,
    114,
    118,
    119
   ],
   [
    1,
    16,
    17,
    18,
    54,
    57,
    70,
    71,
    76,
    116,
    118,
    119,
    123
   ],
   [
    0,
    1,
    16,
    19,
    55,
    56,
    57,
    70,
    77,
    117,
    118,
    122,
    123
   ],
   [
    3,
    18,
    19,
    20,
    56,
    59,
    63,
    72,
    73,
    78,
    118,
    120,
    121
   ],
   [
    4,
    5,
    20,
    23,
    59,
    60,
    61,
    64,
    65,
    74,
    81,
    121,
    122
   ]
  ]
 },
 "distance": {
  "d": 13,
  "X": {
   "value": 13,
   "confidence": "upper_bound",
   "witness": [
    4,
    9,
    12,
    13,
    34,
    41,
    70,
    76,
    78,
    111,
    118,
    122,
    123
   ],
   "witness_provenance": {
    "found_by": [
     "@hirobumii"
    ],
    "date": "2026-10-17",
    "found_at_samples": 1000000,
    "survived_samples": 1000000,
    "tool": "official gf2_fast CSS RIS, per-side trials, pair_depth16, threads1",
    "seeds": [
     20261017712
    ]
   }
  },
  "Z": {
   "value": 13,
   "confidence": "upper_bound",
   "witness": [
    7,
    11,
    23,
    42,
    43,
    48,
    52,
    53,
    64,
    77,
    86,
    103,
    113
   ]
  }
 },
 "provenance": {
  "authors": [
   "@hirobumii"
  ],
  "construction": "GF(4) generalized-bicycle binary expansion, omega^2+omega+1=0, period31; f=[3,2,0,1,0,0,0,0,2,0,0,3], g=[3,1,0,0,1,0,0,0,0,0,0,0,2,3]. rho(omega)=[[0,1],[1,1]], C(p)[i,j]=p[(i-j) mod31], HX=[rho(C(f))|rho(C(g))], HZ=[rho(C(g))^T|rho(C(f))^T]. Multiply each GF4 check by omega, then retain 52 independent binary rows per side; same stabilizer group, all checks weight13, maximum total qubit degree12.",
  "references": [
   "https://arxiv.org/abs/1904.02703v3"
  ],
  "date": "2026-10-17",
  "notes": "No catalog fingerprint or WL match was found at the recorded validation snapshot. Generator reductions preserve the independently reconstructed CSS rowspaces; literature equivalence and novelty remain unverified.",
  "origin": "submission",
  "search_budget": {
   "gpu_hours": 0,
   "notes": "ris_trials_per_side is the deepest single rung; two fresh rungs total2,000,000 per side. Earlier exploratory cost was not measured and is not represented as a total here.",
   "ris_trials_per_side": 1000000
  }
 },
 "family": "generalized-bicycle"
}
