{
 "schema_version": "0.2",
 "name": "[[168,20,10]] CLP code (arXiv:2610.12782 Table I, weight 7)",
 "code_type": "CSS",
 "n": 168,
 "k": 20,
 "checks": {
  "X": [
   [
    0,
    21,
    37,
    84,
    118,
    126,
    148
   ],
   [
    1,
    17,
    40,
    85,
    115,
    127,
    145
   ],
   [
    2,
    3,
    27,
    85,
    86,
    128,
    154
   ],
   [
    3,
    7,
    41,
    87,
    124,
    129,
    156
   ],
   [
    4,
    6,
    23,
    84,
    88,
    130,
    151
   ],
   [
    5,
    18,
    34,
    89,
    125,
    131,
    159
   ],
   [
    6,
    10,
    39,
    90,
    121,
    132,
    152
   ],
   [
    7,
    8,
    33,
    88,
    91,
    133,
    160
   ],
   [
    8,
    9,
    13,
    90,
    92,
    134,
    162
   ],
   [
    9,
    14,
    31,
    93,
    123,
    135,
    155
   ],
   [
    10,
    12,
    29,
    86,
    94,
    136,
    157
   ],
   [
    1,
    11,
    24,
    93,
    95,
    137,
    164
   ],
   [
    5,
    12,
    16,
    87,
    96,
    138,
    158
   ],
   [
    13,
    14,
    38,
    94,
    97,
    127,
    139
   ],
   [
    14,
    15,
    19,
    96,
    98,
    140,
    166
   ],
   [
    0,
    15,
    20,
    89,
    99,
    141,
    161
   ],
   [
    16,
    18,
    35,
    91,
    100,
    126,
    142
   ],
   [
    4,
    17,
    30,
    99,
    101,
    143,
    167
   ],
   [
    11,
    18,
    22,
    92,
    102,
    144,
    163
   ],
   [
    19,
    20,
    41,
    100,
    103,
    130,
    145
   ],
   [
    20,
    21,
    25,
    102,
    104,
    132,
    146
   ],
   [
    2,
    21,
    26,
    95,
    105,
    147,
    165
   ],
   [
    22,
    24,
    39,
    97,
    106,
    128,
    148
   ],
   [
    10,
    23,
    36,
    105,
    107,
    135,
    149
   ],
   [
    17,
    24,
    28,
    98,
    108,
    129,
    150
   ],
   [
    9,
    25,
    26,
    106,
    109,
    136,
    151
   ],
   [
    26,
    27,
    31,
    108,
    110,
    138,
    152
   ],
   [
    7,
    27,
    32,
    101,
    111,
    131,
    153
   ],
   [
    5,
    28,
    30,
    103,
    112,
    133,
    154
   ],
   [
    16,
    29,
    40,
    111,
    113,
    141,
    155
   ],
   [
    23,
    30,
    34,
    104,
    114,
    134,
    156
   ],
   [
    15,
    31,
    32,
    112,
    115,
    142,
    157
   ],
   [
    0,
    32,
    33,
    114,
    116,
    144,
    158
   ],
   [
    13,
    33,
    37,
    107,
    117,
    137,
    159
   ],
   [
    11,
    34,
    36,
    109,
    118,
    139,
    160
   ],
   [
    6,
    22,
    35,
    117,
    119,
    147,
    161
   ],
   [
    1,
    29,
    36,
    110,
    120,
    140,
    162
   ],
   [
    2,
    37,
    38,
    120,
    121,
    150,
    163
   ],
   [
    3,
    19,
    38,
    113,
    122,
    143,
    164
   ],
   [
    12,
    28,
    39,
    122,
    123,
    153,
    165
   ],
   [
    4,
    35,
    40,
    116,
    124,
    146,
    166
   ],
   [
    8,
    25,
    41,
    119,
    125,
    149,
    167
   ],
   [
    42,
    63,
    79,
    84,
    94,
    139,
    151
   ],
   [
    43,
    59,
    82,
    85,
    91,
    142,
    154
   ],
   [
    44,
    45,
    69,
    86,
    100,
    145,
    157
   ],
   [
    45,
    49,
    83,
    87,
    102,
    146,
    158
   ],
   [
    46,
    48,
    65,
    88,
    97,
    148,
    160
   ],
   [
    47,
    60,
    76,
    89,
    105,
    149,
    161
   ],
   [
    48,
    52,
    81,
    90,
    98,
    150,
    162
   ],
   [
    49,
    50,
    75,
    91,
    106,
    126,
    151
   ],
   [
    50,
    51,
    55,
    92,
    108,
    152,
    163
   ],
   [
    51,
    56,
    73,
    93,
    101,
    153,
    164
   ],
   [
    52,
    54,
    71,
    94,
    103,
    127,
    154
   ],
   [
    43,
    53,
    66,
    95,
    111,
    155,
    165
   ],
   [
    47,
    54,
    58,
    96,
    104,
    156,
    166
   ],
   [
    55,
    56,
    80,
    97,
    112,
    128,
    157
   ],
   [
    56,
    57,
    61,
    98,
    114,
    129,
    158
   ],
   [
    42,
    57,
    62,
    99,
    107,
    159,
    167
   ],
   [
    58,
    60,
    77,
    100,
    109,
    130,
    160
   ],
   [
    46,
    59,
    72,
    101,
    117,
    131,
    161
   ],
   [
    53,
    60,
    64,
    102,
    110,
    132,
    162
   ],
   [
    61,
    62,
    83,
    103,
    118,
    126,
    133
   ],
   [
    62,
    63,
    67,
    104,
    120,
    134,
    163
   ],
   [
    44,
    63,
    68,
    105,
    113,
    135,
    164
   ],
   [
    64,
    66,
    81,
    106,
    115,
    127,
    136
   ],
   [
    52,
    65,
    78,
    107,
    122,
    137,
    165
   ],
   [
    59,
    66,
    70,
    108,
    116,
    138,
    166
   ],
   [
    51,
    67,
    68,
    85,
    109,
    128,
    139
   ],
   [
    68,
    69,
    73,
    110,
    124,
    129,
    140
   ],
   [
    49,
    69,
    74,
    111,
    119,
    141,
    167
   ],
   [
    47,
    70,
    72,
    84,
    112,
    130,
    142
   ],
   [
    58,
    71,
    82,
    113,
    125,
    131,
    143
   ],
   [
    65,
    72,
    76,
    114,
    121,
    132,
    144
   ],
   [
    57,
    73,
    74,
    88,
    115,
    133,
    145
   ],
   [
    42,
    74,
    75,
    90,
    116,
    134,
    146
   ],
   [
    55,
    75,
    79,
    117,
    123,
    135,
    147
   ],
   [
    53,
    76,
    78,
    86,
    118,
    136,
    148
   ],
   [
    48,
    64,
    77,
    93,
    119,
    137,
    149
   ],
   [
    43,
    71,
    78,
    87,
    120,
    138,
    150
   ],
   [
    44,
    79,
    80,
    96,
    121,
    140,
    152
   ],
   [
    45,
    61,
    80,
    89,
    122,
    141,
    153
   ],
   [
    54,
    70,
    81,
    99,
    123,
    143,
    155
   ],
   [
    46,
    77,
    82,
    92,
    124,
    144,
    156
   ],
   [
    50,
    67,
    83,
    95,
    125,
    147,
    159
   ]
  ],
  "Z": [
   [
    0,
    4,
    42,
    70,
    84,
    99,
    116
   ],
   [
    1,
    2,
    43,
    67,
    85,
    95,
    120
   ],
   [
    2,
    10,
    44,
    76,
    86,
    105,
    121
   ],
   [
    3,
    12,
    45,
    78,
    86,
    87,
    122
   ],
   [
    4,
    7,
    46,
    73,
    88,
    101,
    124
   ],
   [
    5,
    15,
    47,
    80,
    89,
    96,
    112
   ],
   [
    6,
    8,
    48,
    74,
    88,
    90,
    119
   ],
   [
    7,
    16,
    43,
    49,
    87,
    91,
    111
   ],
   [
    8,
    18,
    50,
    82,
    91,
    92,
    125
   ],
   [
    9,
    11,
    51,
    77,
    92,
    93,
    109
   ],
   [
    10,
    13,
    42,
    52,
    90,
    94,
    107
   ],
   [
    11,
    21,
    53,
    83,
    95,
    102,
    118
   ],
   [
    12,
    14,
    54,
    79,
    94,
    96,
    123
   ],
   [
    13,
    22,
    46,
    55,
    92,
    97,
    117
   ],
   [
    14,
    24,
    48,
    56,
    93,
    97,
    98
   ],
   [
    15,
    17,
    57,
    81,
    98,
    99,
    115
   ],
   [
    16,
    19,
    44,
    58,
    96,
    100,
    113
   ],
   [
    17,
    27,
    51,
    59,
    85,
    101,
    108
   ],
   [
    18,
    20,
    45,
    60,
    89,
    100,
    102
   ],
   [
    19,
    28,
    52,
    61,
    98,
    103,
    122
   ],
   [
    20,
    30,
    54,
    62,
    99,
    103,
    104
   ],
   [
    21,
    23,
    47,
    63,
    84,
    104,
    105
   ],
   [
    22,
    25,
    49,
    64,
    102,
    106,
    119
   ],
   [
    23,
    33,
    57,
    65,
    88,
    107,
    114
   ],
   [
    24,
    26,
    50,
    66,
    95,
    106,
    108
   ],
   [
    25,
    34,
    58,
    67,
    104,
    109,
    125
   ],
   [
    26,
    36,
    60,
    68,
    105,
    109,
    110
   ],
   [
    27,
    29,
    53,
    69,
    86,
    110,
    111
   ],
   [
    28,
    31,
    55,
    70,
    108,
    112,
    123
   ],
   [
    29,
    38,
    63,
    71,
    94,
    113,
    120
   ],
   [
    30,
    32,
    56,
    72,
    101,
    112,
    114
   ],
   [
    1,
    31,
    64,
    73,
    93,
    110,
    115
   ],
   [
    32,
    40,
    66,
    74,
    111,
    115,
    116
   ],
   [
    33,
    35,
    59,
    75,
    91,
    116,
    117
   ],
   [
    0,
    34,
    61,
    76,
    89,
    114,
    118
   ],
   [
    35,
    41,
    69,
    77,
    100,
    119,
    124
   ],
   [
    36,
    37,
    62,
    78,
    107,
    118,
    120
   ],
   [
    6,
    37,
    72,
    79,
    84,
    117,
    121
   ],
   [
    38,
    39,
    65,
    80,
    97,
    121,
    122
   ],
   [
    9,
    39,
    75,
    81,
    90,
    106,
    123
   ],
   [
    3,
    40,
    68,
    82,
    85,
    113,
    124
   ],
   [
    5,
    41,
    71,
    83,
    87,
    103,
    125
   ],
   [
    0,
    16,
    49,
    61,
    126,
    141,
    158
   ],
   [
    1,
    13,
    52,
    64,
    127,
    137,
    162
   ],
   [
    2,
    22,
    55,
    67,
    128,
    147,
    163
   ],
   [
    3,
    24,
    56,
    68,
    128,
    129,
    164
   ],
   [
    4,
    19,
    58,
    70,
    130,
    143,
    166
   ],
   [
    5,
    27,
    59,
    71,
    131,
    138,
    154
   ],
   [
    6,
    20,
    60,
    72,
    130,
    132,
    161
   ],
   [
    7,
    28,
    61,
    73,
    129,
    133,
    153
   ],
   [
    8,
    30,
    62,
    74,
    133,
    134,
    167
   ],
   [
    9,
    23,
    63,
    75,
    134,
    135,
    151
   ],
   [
    10,
    25,
    64,
    76,
    132,
    136,
    149
   ],
   [
    11,
    33,
    65,
    77,
    137,
    144,
    160
   ],
   [
    12,
    26,
    66,
    78,
    136,
    138,
    165
   ],
   [
    13,
    34,
    42,
    67,
    134,
    139,
    159
   ],
   [
    14,
    36,
    68,
    79,
    135,
    139,
    140
   ],
   [
    15,
    29,
    69,
    80,
    140,
    141,
    157
   ],
   [
    16,
    31,
    43,
    70,
    138,
    142,
    155
   ],
   [
    17,
    38,
    71,
    81,
    127,
    143,
    150
   ],
   [
    18,
    32,
    72,
    82,
    131,
    142,
    144
   ],
   [
    1,
    19,
    44,
    73,
    140,
    145,
    164
   ],
   [
    20,
    40,
    45,
    74,
    141,
    145,
    146
   ],
   [
    21,
    35,
    75,
    83,
    126,
    146,
    147
   ],
   [
    0,
    22,
    46,
    76,
    144,
    148,
    161
   ],
   [
    23,
    41,
    47,
    77,
    130,
    149,
    156
   ],
   [
    24,
    37,
    48,
    78,
    137,
    148,
    150
   ],
   [
    4,
    25,
    42,
    49,
    146,
    151,
    167
   ],
   [
    6,
    26,
    50,
    79,
    147,
    151,
    152
   ],
   [
    27,
    39,
    51,
    80,
    128,
    152,
    153
   ],
   [
    2,
    28,
    43,
    52,
    150,
    154,
    165
   ],
   [
    9,
    29,
    53,
    81,
    136,
    155,
    162
   ],
   [
    3,
    30,
    54,
    82,
    143,
    154,
    156
   ],
   [
    10,
    31,
    44,
    55,
    135,
    152,
    157
   ],
   [
    12,
    32,
    45,
    56,
    153,
    157,
    158
   ],
   [
    5,
    33,
    57,
    83,
    133,
    158,
    159
   ],
   [
    7,
    34,
    46,
    58,
    131,
    156,
    160
   ],
   [
    15,
    35,
    47,
    59,
    142,
    161,
    166
   ],
   [
    8,
    36,
    48,
    60,
    149,
    160,
    162
   ],
   [
    18,
    37,
    50,
    62,
    126,
    159,
    163
   ],
   [
    11,
    38,
    51,
    63,
    139,
    163,
    164
   ],
   [
    21,
    39,
    53,
    65,
    132,
    148,
    165
   ],
   [
    14,
    40,
    54,
    66,
    127,
    155,
    166
   ],
   [
    17,
    41,
    57,
    69,
    129,
    145,
    167
   ]
  ]
 },
 "distance": {
  "d": 10,
  "X": {
   "value": 10,
   "confidence": "upper_bound",
   "witness": [
    0,
    2,
    10,
    22,
    25,
    28,
    42,
    55,
    61,
    67
   ],
   "witness_provenance": {
    "found_by": [
     "@MathysRennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 4000,
    "survived_samples": 4000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     11
    ]
   }
  },
  "Z": {
   "value": 10,
   "confidence": "upper_bound",
   "witness": [
    51,
    55,
    56,
    61,
    62,
    67,
    89,
    117,
    159,
    161
   ],
   "witness_provenance": {
    "found_by": [
     "@MathysRennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 4000,
    "survived_samples": 4000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     12
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Rajpurohit, Rajendra Prasad",
   "Lalitha, V.",
   "Garani, Shayan Srinivasa",
   "@MathysRennela"
  ],
  "construction": "Coset lifted product (CLP) code of arXiv:2610.12782, Definition III.1, 1x1 over 2x2 layout: a protograph A over F_2[G] acting by the LEFT coset action of G on the cosets G/H, and a protograph B over F_2[N_G(H)] acting by the RIGHT coset action of the normaliser on the same cosets. G = SmallGroup(336,188), H = <f1*f2, f2*f3, f5> (non-normal, core free), m = [G:H], n = 4m = 168. Elements are named by the polycyclic generating sequence f_1,...,f_r of SmallGroup(336,188), as in the paper's Appendix A. CSS commutation is automatic (L(g) and R(n) commute for every g in G and n in N_G(H), so each block of H_X H_Z^T is L R + R L = 0 over F_2); no search for it is needed. n, k and the check weight 7 reproduce the paper's Table I exactly. Literature baseline seeded from the published parameters: this entry is a REPRODUCTION built from the paper's printed data, not a new construction and not a new parameter set. The paper certifies d = 10 by integer program; this entry carries witness-backed upper bounds from our own randomized GF(2) search, which is a weaker claim.",
  "references": [
   "arXiv:2610.12782",
   "arXiv:2606.17268"
  ],
  "date": "2026-10-12",
  "notes": "Literature baseline: a reproduction of the published parameters in arXiv:2610.12782 (Table I), not a new construction and not a new parameter set. The group, subgroup and protographs are the paper's Appendix A data, rebuilt from GAP SmallGroup(l,i); n, k and the check weight reproduce the paper exactly. Reproduced by Space Bunny Alpha 1.0. The distance here is a witness-backed upper bound from our own randomized GF(2) search, a weaker claim than the paper's integer-program certification. See the accompanying note for the full reproduction recipe.",
  "origin": "baseline",
  "novelty": "known_parameters",
  "model": "Space Bunny Alpha 1.0"
 },
 "family": "2bga-coset"
}