{
 "schema_version": "0.2",
 "name": "[[88,2,14]] two-block code over D44",
 "code_type": "CSS",
 "n": 88,
 "k": 2,
 "checks": {
  "X": [
   [
    0,
    1,
    22,
    39,
    44,
    55,
    75,
    86
   ],
   [
    0,
    1,
    5,
    28,
    45,
    57,
    77,
    87
   ],
   [
    2,
    4,
    19,
    42,
    46,
    58,
    78,
    83
   ],
   [
    0,
    3,
    5,
    26,
    46,
    47,
    59,
    79
   ],
   [
    2,
    4,
    8,
    25,
    48,
    60,
    80,
    85
   ],
   [
    3,
    5,
    9,
    32,
    48,
    49,
    61,
    81
   ],
   [
    2,
    6,
    8,
    23,
    44,
    50,
    62,
    82
   ],
   [
    3,
    7,
    9,
    30,
    50,
    51,
    63,
    83
   ],
   [
    6,
    8,
    12,
    29,
    45,
    52,
    64,
    84
   ],
   [
    7,
    9,
    13,
    36,
    52,
    53,
    65,
    85
   ],
   [
    6,
    10,
    12,
    27,
    47,
    54,
    66,
    86
   ],
   [
    7,
    11,
    13,
    34,
    44,
    54,
    55,
    67
   ],
   [
    10,
    12,
    16,
    33,
    49,
    56,
    68,
    87
   ],
   [
    11,
    13,
    17,
    40,
    45,
    56,
    57,
    69
   ],
   [
    10,
    14,
    16,
    31,
    46,
    51,
    58,
    70
   ],
   [
    11,
    15,
    17,
    38,
    47,
    58,
    59,
    71
   ],
   [
    14,
    16,
    20,
    37,
    48,
    53,
    60,
    72
   ],
   [
    15,
    17,
    21,
    43,
    49,
    60,
    61,
    73
   ],
   [
    14,
    18,
    20,
    35,
    50,
    55,
    62,
    74
   ],
   [
    15,
    19,
    21,
    42,
    51,
    62,
    63,
    75
   ],
   [
    18,
    20,
    24,
    41,
    52,
    57,
    64,
    76
   ],
   [
    4,
    19,
    21,
    25,
    53,
    64,
    65,
    77
   ],
   [
    18,
    22,
    24,
    39,
    54,
    59,
    66,
    78
   ],
   [
    2,
    19,
    23,
    25,
    55,
    66,
    67,
    79
   ],
   [
    1,
    22,
    24,
    28,
    56,
    61,
    68,
    80
   ],
   [
    8,
    23,
    25,
    29,
    57,
    68,
    69,
    81
   ],
   [
    0,
    22,
    26,
    28,
    58,
    63,
    70,
    82
   ],
   [
    6,
    23,
    27,
    29,
    59,
    70,
    71,
    83
   ],
   [
    5,
    26,
    28,
    32,
    60,
    65,
    72,
    84
   ],
   [
    12,
    27,
    29,
    33,
    61,
    72,
    73,
    85
   ],
   [
    3,
    26,
    30,
    32,
    62,
    67,
    74,
    86
   ],
   [
    10,
    27,
    31,
    33,
    44,
    63,
    74,
    75
   ],
   [
    9,
    30,
    32,
    36,
    64,
    69,
    76,
    87
   ],
   [
    16,
    31,
    33,
    37,
    45,
    65,
    76,
    77
   ],
   [
    7,
    30,
    34,
    36,
    46,
    66,
    71,
    78
   ],
   [
    14,
    31,
    35,
    37,
    47,
    67,
    78,
    79
   ],
   [
    13,
    34,
    36,
    40,
    48,
    68,
    73,
    80
   ],
   [
    20,
    35,
    37,
    41,
    49,
    69,
    80,
    81
   ],
   [
    11,
    34,
    38,
    40,
    50,
    70,
    75,
    82
   ],
   [
    18,
    35,
    39,
    41,
    51,
    71,
    82,
    83
   ],
   [
    17,
    38,
    40,
    43,
    52,
    72,
    77,
    84
   ],
   [
    1,
    24,
    39,
    41,
    53,
    73,
    84,
    85
   ],
   [
    15,
    38,
    42,
    43,
    54,
    74,
    79,
    86
   ],
   [
    4,
    21,
    42,
    43,
    56,
    76,
    81,
    87
   ]
  ],
  "Z": [
   [
    0,
    6,
    11,
    31,
    44,
    45,
    47,
    70
   ],
   [
    1,
    8,
    13,
    33,
    44,
    45,
    68,
    85
   ],
   [
    2,
    3,
    14,
    34,
    46,
    48,
    50,
    67
   ],
   [
    3,
    10,
    15,
    35,
    47,
    49,
    51,
    74
   ],
   [
    4,
    5,
    16,
    36,
    46,
    48,
    65,
    87
   ],
   [
    5,
    12,
    17,
    37,
    45,
    47,
    49,
    72
   ],
   [
    6,
    7,
    18,
    38,
    50,
    52,
    54,
    71
   ],
   [
    7,
    14,
    19,
    39,
    51,
    53,
    55,
    78
   ],
   [
    8,
    9,
    20,
    40,
    48,
    50,
    52,
    69
   ],
   [
    9,
    16,
    21,
    41,
    49,
    51,
    53,
    76
   ],
   [
    10,
    11,
    22,
    42,
    54,
    56,
    58,
    75
   ],
   [
    0,
    11,
    18,
    23,
    55,
    57,
    59,
    82
   ],
   [
    12,
    13,
    24,
    43,
    52,
    54,
    56,
    73
   ],
   [
    1,
    13,
    20,
    25,
    53,
    55,
    57,
    80
   ],
   [
    2,
    14,
    15,
    26,
    58,
    60,
    62,
    79
   ],
   [
    3,
    15,
    22,
    27,
    59,
    61,
    63,
    86
   ],
   [
    4,
    16,
    17,
    28,
    56,
    58,
    60,
    77
   ],
   [
    5,
    17,
    24,
    29,
    57,
    59,
    61,
    84
   ],
   [
    6,
    18,
    19,
    30,
    62,
    64,
    66,
    83
   ],
   [
    7,
    19,
    26,
    31,
    46,
    63,
    65,
    67
   ],
   [
    8,
    20,
    21,
    32,
    60,
    62,
    64,
    81
   ],
   [
    9,
    21,
    28,
    33,
    61,
    63,
    65,
    87
   ],
   [
    10,
    22,
    23,
    34,
    44,
    66,
    68,
    70
   ],
   [
    11,
    23,
    30,
    35,
    50,
    67,
    69,
    71
   ],
   [
    12,
    24,
    25,
    36,
    64,
    66,
    68,
    85
   ],
   [
    13,
    25,
    32,
    37,
    48,
    65,
    67,
    69
   ],
   [
    14,
    26,
    27,
    38,
    47,
    70,
    72,
    74
   ],
   [
    15,
    27,
    34,
    39,
    54,
    71,
    73,
    75
   ],
   [
    16,
    28,
    29,
    40,
    45,
    68,
    70,
    72
   ],
   [
    17,
    29,
    36,
    41,
    52,
    69,
    71,
    73
   ],
   [
    18,
    30,
    31,
    42,
    51,
    74,
    76,
    78
   ],
   [
    0,
    19,
    31,
    38,
    58,
    75,
    77,
    79
   ],
   [
    20,
    32,
    33,
    43,
    49,
    72,
    74,
    76
   ],
   [
    1,
    21,
    33,
    40,
    56,
    73,
    75,
    77
   ],
   [
    2,
    22,
    34,
    35,
    55,
    78,
    80,
    82
   ],
   [
    3,
    23,
    35,
    42,
    62,
    79,
    81,
    83
   ],
   [
    4,
    24,
    36,
    37,
    53,
    76,
    78,
    80
   ],
   [
    5,
    25,
    37,
    43,
    60,
    77,
    79,
    81
   ],
   [
    6,
    26,
    38,
    39,
    59,
    82,
    84,
    86
   ],
   [
    2,
    7,
    27,
    39,
    44,
    66,
    83,
    85
   ],
   [
    8,
    28,
    40,
    41,
    57,
    80,
    82,
    84
   ],
   [
    4,
    9,
    29,
    41,
    64,
    81,
    83,
    85
   ],
   [
    0,
    10,
    30,
    42,
    46,
    63,
    86,
    87
   ],
   [
    1,
    12,
    32,
    43,
    61,
    84,
    86,
    87
   ]
  ]
 },
 "distance": {
  "d": 14,
  "X": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    3,
    28,
    31,
    32,
    33,
    40,
    45,
    48,
    60,
    63,
    72,
    74,
    79,
    87
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1039
    ]
   }
  },
  "Z": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    10,
    12,
    23,
    25,
    33,
    41,
    48,
    49,
    52,
    65,
    70,
    72,
    73,
    82
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1040
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over D44 = SmallGroup(44, 3) (order 44), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 88; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 1, 3, 26}, b = {0, 6, 11, 31} as element indices. Check weight 8. 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": "2bga-nonabelian",
 "locality": {
  "coordinates": [
   [
    4.0,
    0.0
   ],
   [
    0.0,
    3.0
   ],
   [
    5.0,
    3.0
   ],
   [
    5.0,
    2.0
   ],
   [
    0.0,
    2.0
   ],
   [
    3.0,
    3.0
   ],
   [
    6.0,
    5.0
   ],
   [
    4.0,
    5.0
   ],
   [
    4.0,
    2.0
   ],
   [
    0.0,
    3.0
   ],
   [
    3.0,
    3.0
   ],
   [
    4.0,
    2.0
   ],
   [
    1.0,
    4.0
   ],
   [
    0.0,
    4.0
   ],
   [
    5.0,
    4.0
   ],
   [
    6.0,
    2.0
   ],
   [
    1.0,
    1.0
   ],
   [
    2.0,
    4.0
   ],
   [
    6.0,
    5.0
   ],
   [
    4.0,
    1.0
   ],
   [
    1.0,
    2.0
   ],
   [
    1.0,
    0.0
   ],
   [
    3.0,
    5.0
   ],
   [
    4.0,
    6.0
   ],
   [
    1.0,
    5.0
   ],
   [
    3.0,
    2.0
   ],
   [
    5.0,
    0.0
   ],
   [
    6.0,
    4.0
   ],
   [
    0.0,
    1.0
   ],
   [
    2.0,
    6.0
   ],
   [
    2.0,
    2.0
   ],
   [
    5.0,
    0.0
   ],
   [
    1.0,
    0.0
   ],
   [
    2.0,
    0.0
   ],
   [
    3.0,
    6.0
   ],
   [
    5.0,
    5.0
   ],
   [
    0.0,
    5.0
   ],
   [
    3.0,
    1.0
   ],
   [
    6.0,
    3.0
   ],
   [
    4.0,
    5.0
   ],
   [
    1.0,
    2.0
   ],
   [
    1.0,
    6.0
   ],
   [
    3.0,
    2.0
   ],
   [
    2.0,
    0.0
   ],
   [
    5.0,
    5.0
   ],
   [
    4.0,
    1.0
   ],
   [
    2.0,
    4.0
   ],
   [
    6.0,
    1.0
   ],
   [
    0.0,
    2.0
   ],
   [
    2.0,
    1.0
   ],
   [
    3.0,
    5.0
   ],
   [
    2.0,
    2.0
   ],
   [
    2.0,
    5.0
   ],
   [
    2.0,
    5.0
   ],
   [
    2.0,
    3.0
   ],
   [
    4.0,
    6.0
   ],
   [
    0.0,
    1.0
   ],
   [
    4.0,
    3.0
   ],
   [
    5.0,
    1.0
   ],
   [
    5.0,
    3.0
   ],
   [
    2.0,
    1.0
   ],
   [
    3.0,
    4.0
   ],
   [
    6.0,
    2.0
   ],
   [
    3.0,
    0.0
   ],
   [
    1.0,
    3.0
   ],
   [
    1.0,
    1.0
   ],
   [
    3.0,
    4.0
   ],
   [
    1.0,
    3.0
   ],
   [
    1.0,
    5.0
   ],
   [
    0.0,
    4.0
   ],
   [
    4.0,
    4.0
   ],
   [
    5.0,
    6.0
   ],
   [
    5.0,
    2.0
   ],
   [
    4.0,
    3.0
   ],
   [
    6.0,
    1.0
   ],
   [
    5.0,
    1.0
   ],
   [
    3.0,
    1.0
   ],
   [
    3.0,
    0.0
   ],
   [
    5.0,
    4.0
   ],
   [
    6.0,
    3.0
   ],
   [
    0.0,
    5.0
   ],
   [
    1.0,
    4.0
   ],
   [
    4.0,
    4.0
   ],
   [
    3.0,
    6.0
   ],
   [
    2.0,
    3.0
   ],
   [
    2.0,
    6.0
   ],
   [
    4.0,
    0.0
   ],
   [
    0.0,
    0.0
   ]
  ],
  "layers": 2,
  "interaction_radius": 6.0,
  "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."
  }
 }
}