{
 "schema_version": "0.1",
 "name": "[[87,22,3]] HP ham15xsham5",
 "code_type": "CSS",
 "n": 87,
 "k": 22,
 "checks": {
  "X": [
   [
    0,
    10,
    20,
    30,
    40,
    50,
    60,
    70,
    75,
    76
   ],
   [
    1,
    11,
    21,
    31,
    41,
    51,
    61,
    71,
    77
   ],
   [
    2,
    12,
    22,
    32,
    42,
    52,
    62,
    72,
    75,
    77
   ],
   [
    3,
    13,
    23,
    33,
    43,
    53,
    63,
    73,
    76,
    77
   ],
   [
    4,
    14,
    24,
    34,
    44,
    54,
    64,
    74,
    75,
    76,
    77
   ],
   [
    5,
    10,
    25,
    30,
    45,
    50,
    65,
    70,
    78,
    79
   ],
   [
    6,
    11,
    26,
    31,
    46,
    51,
    66,
    71,
    80
   ],
   [
    7,
    12,
    27,
    32,
    47,
    52,
    67,
    72,
    78,
    80
   ],
   [
    8,
    13,
    28,
    33,
    48,
    53,
    68,
    73,
    79,
    80
   ],
   [
    9,
    14,
    29,
    34,
    49,
    54,
    69,
    74,
    78,
    79,
    80
   ],
   [
    15,
    20,
    25,
    30,
    55,
    60,
    65,
    70,
    81,
    82
   ],
   [
    16,
    21,
    26,
    31,
    56,
    61,
    66,
    71,
    83
   ],
   [
    17,
    22,
    27,
    32,
    57,
    62,
    67,
    72,
    81,
    83
   ],
   [
    18,
    23,
    28,
    33,
    58,
    63,
    68,
    73,
    82,
    83
   ],
   [
    19,
    24,
    29,
    34,
    59,
    64,
    69,
    74,
    81,
    82,
    83
   ],
   [
    35,
    40,
    45,
    50,
    55,
    60,
    65,
    70,
    84,
    85
   ],
   [
    36,
    41,
    46,
    51,
    56,
    61,
    66,
    71,
    86
   ],
   [
    37,
    42,
    47,
    52,
    57,
    62,
    67,
    72,
    84,
    86
   ],
   [
    38,
    43,
    48,
    53,
    58,
    63,
    68,
    73,
    85,
    86
   ],
   [
    39,
    44,
    49,
    54,
    59,
    64,
    69,
    74,
    84,
    85,
    86
   ]
  ],
  "Z": [
   [
    0,
    2,
    4,
    75
   ],
   [
    0,
    3,
    4,
    76
   ],
   [
    1,
    2,
    3,
    4,
    77
   ],
   [
    5,
    7,
    9,
    78
   ],
   [
    5,
    8,
    9,
    79
   ],
   [
    6,
    7,
    8,
    9,
    80
   ],
   [
    10,
    12,
    14,
    75,
    78
   ],
   [
    10,
    13,
    14,
    76,
    79
   ],
   [
    11,
    12,
    13,
    14,
    77,
    80
   ],
   [
    15,
    17,
    19,
    81
   ],
   [
    15,
    18,
    19,
    82
   ],
   [
    16,
    17,
    18,
    19,
    83
   ],
   [
    20,
    22,
    24,
    75,
    81
   ],
   [
    20,
    23,
    24,
    76,
    82
   ],
   [
    21,
    22,
    23,
    24,
    77,
    83
   ],
   [
    25,
    27,
    29,
    78,
    81
   ],
   [
    25,
    28,
    29,
    79,
    82
   ],
   [
    26,
    27,
    28,
    29,
    80,
    83
   ],
   [
    30,
    32,
    34,
    75,
    78,
    81
   ],
   [
    30,
    33,
    34,
    76,
    79,
    82
   ],
   [
    31,
    32,
    33,
    34,
    77,
    80,
    83
   ],
   [
    35,
    37,
    39,
    84
   ],
   [
    35,
    38,
    39,
    85
   ],
   [
    36,
    37,
    38,
    39,
    86
   ],
   [
    40,
    42,
    44,
    75,
    84
   ],
   [
    40,
    43,
    44,
    76,
    85
   ],
   [
    41,
    42,
    43,
    44,
    77,
    86
   ],
   [
    45,
    47,
    49,
    78,
    84
   ],
   [
    45,
    48,
    49,
    79,
    85
   ],
   [
    46,
    47,
    48,
    49,
    80,
    86
   ],
   [
    50,
    52,
    54,
    75,
    78,
    84
   ],
   [
    50,
    53,
    54,
    76,
    79,
    85
   ],
   [
    51,
    52,
    53,
    54,
    77,
    80,
    86
   ],
   [
    55,
    57,
    59,
    81,
    84
   ],
   [
    55,
    58,
    59,
    82,
    85
   ],
   [
    56,
    57,
    58,
    59,
    83,
    86
   ],
   [
    60,
    62,
    64,
    75,
    81,
    84
   ],
   [
    60,
    63,
    64,
    76,
    82,
    85
   ],
   [
    61,
    62,
    63,
    64,
    77,
    83,
    86
   ],
   [
    65,
    67,
    69,
    78,
    81,
    84
   ],
   [
    65,
    68,
    69,
    79,
    82,
    85
   ],
   [
    66,
    67,
    68,
    69,
    80,
    83,
    86
   ],
   [
    70,
    72,
    74,
    75,
    78,
    81,
    84
   ],
   [
    70,
    73,
    74,
    76,
    79,
    82,
    85
   ],
   [
    71,
    72,
    73,
    74,
    77,
    80,
    83,
    86
   ]
  ]
 },
 "distance": {
  "d": 3,
  "X": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
    45,
    46,
    49
   ]
  },
  "Z": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
    33,
    48,
    63
   ]
  }
 },
 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "Hypergraph product of classical codes ham15 and sham5",
  "origin": "submission",
  "date": "2026-07-17",
  "references": [
   "arXiv:0903.0566"
  ],
  "model": "Tencent Hy3"
 },
 "family": "hypergraph-product"
}
