{
 "schema_version": "0.3",
 "name": "[[112,12,8]]",
 "code_type": "CSS",
 "n": 112,
 "k": 12,
 "checks": {
  "X": [
   [
    0,
    51,
    54,
    56,
    72,
    108
   ],
   [
    1,
    50,
    55,
    57,
    73,
    109
   ],
   [
    0,
    2,
    53,
    58,
    74,
    110
   ],
   [
    1,
    3,
    52,
    59,
    75,
    111
   ],
   [
    2,
    4,
    55,
    56,
    60,
    76
   ],
   [
    3,
    5,
    54,
    57,
    61,
    77
   ],
   [
    1,
    4,
    6,
    58,
    62,
    78
   ],
   [
    0,
    5,
    7,
    59,
    63,
    79
   ],
   [
    3,
    6,
    8,
    60,
    64,
    80
   ],
   [
    2,
    7,
    9,
    61,
    65,
    81
   ],
   [
    5,
    8,
    10,
    62,
    66,
    82
   ],
   [
    4,
    9,
    11,
    63,
    67,
    83
   ],
   [
    7,
    10,
    12,
    64,
    68,
    84
   ],
   [
    6,
    11,
    13,
    65,
    69,
    85
   ],
   [
    9,
    12,
    14,
    66,
    70,
    86
   ],
   [
    8,
    13,
    15,
    67,
    71,
    87
   ],
   [
    11,
    14,
    16,
    68,
    72,
    88
   ],
   [
    10,
    15,
    17,
    69,
    73,
    89
   ],
   [
    13,
    16,
    18,
    70,
    74,
    90
   ],
   [
    12,
    17,
    19,
    71,
    75,
    91
   ],
   [
    15,
    18,
    20,
    72,
    76,
    92
   ],
   [
    14,
    19,
    21,
    73,
    77,
    93
   ],
   [
    17,
    20,
    22,
    74,
    78,
    94
   ],
   [
    16,
    21,
    23,
    75,
    79,
    95
   ],
   [
    19,
    22,
    24,
    76,
    80,
    96
   ],
   [
    18,
    23,
    25,
    77,
    81,
    97
   ],
   [
    21,
    24,
    26,
    78,
    82,
    98
   ],
   [
    20,
    25,
    27,
    79,
    83,
    99
   ],
   [
    23,
    26,
    28,
    80,
    84,
    100
   ],
   [
    22,
    27,
    29,
    81,
    85,
    101
   ],
   [
    25,
    28,
    30,
    82,
    86,
    102
   ],
   [
    24,
    29,
    31,
    83,
    87,
    103
   ],
   [
    27,
    30,
    32,
    84,
    88,
    104
   ],
   [
    26,
    31,
    33,
    85,
    89,
    105
   ],
   [
    29,
    32,
    34,
    86,
    90,
    106
   ],
   [
    28,
    33,
    35,
    87,
    91,
    107
   ],
   [
    31,
    34,
    36,
    88,
    92,
    108
   ],
   [
    30,
    35,
    37,
    89,
    93,
    109
   ],
   [
    33,
    36,
    38,
    90,
    94,
    110
   ],
   [
    32,
    37,
    39,
    91,
    95,
    111
   ],
   [
    35,
    38,
    40,
    56,
    92,
    96
   ],
   [
    34,
    39,
    41,
    57,
    93,
    97
   ],
   [
    37,
    40,
    42,
    58,
    94,
    98
   ],
   [
    36,
    41,
    43,
    59,
    95,
    99
   ],
   [
    39,
    42,
    44,
    60,
    96,
    100
   ],
   [
    38,
    43,
    45,
    61,
    97,
    101
   ],
   [
    41,
    44,
    46,
    62,
    98,
    102
   ],
   [
    40,
    45,
    47,
    63,
    99,
    103
   ],
   [
    43,
    46,
    48,
    64,
    100,
    104
   ],
   [
    42,
    47,
    49,
    65,
    101,
    105
   ],
   [
    45,
    48,
    50,
    66,
    102,
    106
   ],
   [
    44,
    49,
    51,
    67,
    103,
    107
   ],
   [
    47,
    50,
    52,
    68,
    104,
    108
   ],
   [
    46,
    51,
    53,
    69,
    105,
    109
   ],
   [
    49,
    52,
    54,
    70,
    106,
    110
   ],
   [
    48,
    53,
    55,
    71,
    107,
    111
   ]
  ],
  "Z": [
   [
    0,
    4,
    40,
    56,
    58,
    63
   ],
   [
    1,
    5,
    41,
    57,
    59,
    62
   ],
   [
    2,
    6,
    42,
    58,
    60,
    65
   ],
   [
    3,
    7,
    43,
    59,
    61,
    64
   ],
   [
    4,
    8,
    44,
    60,
    62,
    67
   ],
   [
    5,
    9,
    45,
    61,
    63,
    66
   ],
   [
    6,
    10,
    46,
    62,
    64,
    69
   ],
   [
    7,
    11,
    47,
    63,
    65,
    68
   ],
   [
    8,
    12,
    48,
    64,
    66,
    71
   ],
   [
    9,
    13,
    49,
    65,
    67,
    70
   ],
   [
    10,
    14,
    50,
    66,
    68,
    73
   ],
   [
    11,
    15,
    51,
    67,
    69,
    72
   ],
   [
    12,
    16,
    52,
    68,
    70,
    75
   ],
   [
    13,
    17,
    53,
    69,
    71,
    74
   ],
   [
    14,
    18,
    54,
    70,
    72,
    77
   ],
   [
    15,
    19,
    55,
    71,
    73,
    76
   ],
   [
    0,
    16,
    20,
    72,
    74,
    79
   ],
   [
    1,
    17,
    21,
    73,
    75,
    78
   ],
   [
    2,
    18,
    22,
    74,
    76,
    81
   ],
   [
    3,
    19,
    23,
    75,
    77,
    80
   ],
   [
    4,
    20,
    24,
    76,
    78,
    83
   ],
   [
    5,
    21,
    25,
    77,
    79,
    82
   ],
   [
    6,
    22,
    26,
    78,
    80,
    85
   ],
   [
    7,
    23,
    27,
    79,
    81,
    84
   ],
   [
    8,
    24,
    28,
    80,
    82,
    87
   ],
   [
    9,
    25,
    29,
    81,
    83,
    86
   ],
   [
    10,
    26,
    30,
    82,
    84,
    89
   ],
   [
    11,
    27,
    31,
    83,
    85,
    88
   ],
   [
    12,
    28,
    32,
    84,
    86,
    91
   ],
   [
    13,
    29,
    33,
    85,
    87,
    90
   ],
   [
    14,
    30,
    34,
    86,
    88,
    93
   ],
   [
    15,
    31,
    35,
    87,
    89,
    92
   ],
   [
    16,
    32,
    36,
    88,
    90,
    95
   ],
   [
    17,
    33,
    37,
    89,
    91,
    94
   ],
   [
    18,
    34,
    38,
    90,
    92,
    97
   ],
   [
    19,
    35,
    39,
    91,
    93,
    96
   ],
   [
    20,
    36,
    40,
    92,
    94,
    99
   ],
   [
    21,
    37,
    41,
    93,
    95,
    98
   ],
   [
    22,
    38,
    42,
    94,
    96,
    101
   ],
   [
    23,
    39,
    43,
    95,
    97,
    100
   ],
   [
    24,
    40,
    44,
    96,
    98,
    103
   ],
   [
    25,
    41,
    45,
    97,
    99,
    102
   ],
   [
    26,
    42,
    46,
    98,
    100,
    105
   ],
   [
    27,
    43,
    47,
    99,
    101,
    104
   ],
   [
    28,
    44,
    48,
    100,
    102,
    107
   ],
   [
    29,
    45,
    49,
    101,
    103,
    106
   ],
   [
    30,
    46,
    50,
    102,
    104,
    109
   ],
   [
    31,
    47,
    51,
    103,
    105,
    108
   ],
   [
    32,
    48,
    52,
    104,
    106,
    111
   ],
   [
    33,
    49,
    53,
    105,
    107,
    110
   ],
   [
    34,
    50,
    54,
    57,
    106,
    108
   ],
   [
    35,
    51,
    55,
    56,
    107,
    109
   ],
   [
    0,
    36,
    52,
    59,
    108,
    110
   ],
   [
    1,
    37,
    53,
    58,
    109,
    111
   ],
   [
    2,
    38,
    54,
    56,
    61,
    110
   ],
   [
    3,
    39,
    55,
    57,
    60,
    111
   ]
  ]
 },
 "distance": {
  "d": 8,
  "X": {
   "value": 8,
   "confidence": "upper_bound",
   "witness": [
    8,
    12,
    28,
    48,
    52,
    59,
    62,
    64
   ]
  },
  "Z": {
   "value": 8,
   "confidence": "upper_bound",
   "witness": [
    49,
    51,
    54,
    57,
    73,
    89,
    93,
    105
   ]
  }
 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "construction": "Two-block group-algebra code on the abelian group Z_28 x Z_2 as built by research/kit/group_algebra.py cyclic_product(28, 2) (element tuple (i, j) at index i*2 + j); supports a = [0, 2, 7] (left regular representation) and b = [0, 4, 40] (right regular representation); H_X = [L(a) | R(b)], H_Z = [R(b)^T | L(a)^T] (research/kit/group_algebra.py build_2bga).",
  "origin": "submission",
  "date": "2026-09-20",
  "model": "Claude Fable 5.1",
  "notes": "Found by a random support sweep over weight-6 two-block group-algebra codes with n <= 160 (a sweep script kept with the search run (not committed; method in the research note)). Distance is a witness-backed upper bound; surrogate ladder [(200000, 8), (1000000, 8)] trials per side. Advances the weight-6 x unrestricted board; novelty vs the literature unverified.",
  "search_budget": {
   "candidates_screened": 99000,
   "ris_trials_per_side": 1000000,
   "wall_clock_hours": 1.0,
   "tool": "research/kit search funnel, gf2_fast RIS"
  }
 },
 "family": "generalized-bicycle"
}
