{
 "schema_version": "0.1",
 "name": "[[103,30,7]] shortened pair-partition CPM code",
 "code_type": "CSS",
 "n": 103,
 "k": 30,
 "checks": {
  "X": [
   [
    7,
    8,
    9,
    10,
    11,
    12,
    13,
    14
   ],
   [
    15,
    16,
    17,
    18,
    19,
    20,
    21,
    22
   ],
   [
    23,
    24,
    25,
    26,
    27,
    28,
    29,
    30
   ],
   [
    31,
    32,
    33,
    34,
    35,
    36,
    37,
    38
   ],
   [
    39,
    40,
    41,
    42,
    43,
    44,
    45,
    46
   ],
   [
    47,
    48,
    49,
    50,
    51,
    52,
    53,
    54
   ],
   [
    55,
    56,
    57,
    58,
    59,
    60,
    61,
    62
   ],
   [
    63,
    64,
    65,
    66,
    67,
    68,
    69,
    70
   ],
   [
    71,
    72,
    73,
    74,
    75,
    76,
    77,
    78
   ],
   [
    79,
    80,
    81,
    82,
    83,
    84,
    85,
    86
   ],
   [
    87,
    88,
    89,
    90,
    91,
    92,
    93,
    94
   ],
   [
    95,
    96,
    97,
    98,
    99,
    100,
    101,
    102
   ],
   [
    0,
    1,
    2,
    3,
    4,
    5,
    6,
    12,
    17,
    48,
    61,
    66,
    86,
    91
   ],
   [
    7,
    20,
    25,
    56,
    69,
    74,
    94,
    99
   ],
   [
    3,
    15,
    28,
    33,
    64,
    77,
    82,
    102
   ],
   [
    6,
    11,
    23,
    36,
    41,
    72,
    85,
    90
   ],
   [
    14,
    19,
    31,
    44,
    49,
    80,
    93,
    98
   ],
   [
    2,
    22,
    27,
    39,
    52,
    57,
    88,
    101
   ],
   [
    5,
    10,
    30,
    35,
    47,
    60,
    65,
    96
   ],
   [
    0,
    13,
    18,
    38,
    43,
    55,
    68,
    73
   ],
   [
    8,
    21,
    26,
    46,
    51,
    63,
    76,
    81
   ],
   [
    16,
    29,
    34,
    54,
    59,
    71,
    84,
    89
   ],
   [
    24,
    37,
    42,
    62,
    67,
    79,
    92,
    97
   ],
   [
    1,
    32,
    45,
    50,
    70,
    75,
    87,
    100
   ],
   [
    4,
    9,
    40,
    53,
    58,
    78,
    83,
    95
   ],
   [
    0,
    1,
    2,
    3,
    4,
    5,
    6,
    34,
    46,
    49,
    68,
    77,
    88,
    99
   ],
   [
    3,
    7,
    42,
    54,
    57,
    76,
    85,
    96
   ],
   [
    0,
    11,
    15,
    50,
    62,
    65,
    84,
    93
   ],
   [
    8,
    19,
    23,
    58,
    70,
    73,
    92,
    101
   ],
   [
    5,
    16,
    27,
    31,
    66,
    78,
    81,
    100
   ],
   [
    4,
    13,
    24,
    35,
    39,
    74,
    86,
    89
   ],
   [
    12,
    21,
    32,
    43,
    47,
    82,
    94,
    97
   ],
   [
    1,
    20,
    29,
    40,
    51,
    55,
    90,
    102
   ],
   [
    6,
    9,
    28,
    37,
    48,
    59,
    63,
    98
   ],
   [
    2,
    14,
    17,
    36,
    45,
    56,
    67,
    71
   ],
   [
    10,
    22,
    25,
    44,
    53,
    64,
    75,
    79
   ],
   [
    18,
    30,
    33,
    52,
    61,
    72,
    83,
    87
   ],
   [
    26,
    38,
    41,
    60,
    69,
    80,
    91,
    95
   ]
  ],
  "Z": [
   [
    6,
    9,
    12,
    72,
    77,
    82,
    83
   ],
   [
    7,
    14,
    17,
    20,
    80,
    85,
    90,
    91
   ],
   [
    15,
    22,
    25,
    28,
    88,
    93,
    98,
    99
   ],
   [
    2,
    3,
    23,
    30,
    33,
    36,
    96,
    101
   ],
   [
    0,
    5,
    10,
    11,
    31,
    38,
    41,
    44
   ],
   [
    8,
    13,
    18,
    19,
    39,
    46,
    49,
    52
   ],
   [
    16,
    21,
    26,
    27,
    47,
    54,
    57,
    60
   ],
   [
    24,
    29,
    34,
    35,
    55,
    62,
    65,
    68
   ],
   [
    32,
    37,
    42,
    43,
    63,
    70,
    73,
    76
   ],
   [
    40,
    45,
    50,
    51,
    71,
    78,
    81,
    84
   ],
   [
    48,
    53,
    58,
    59,
    79,
    86,
    89,
    92
   ],
   [
    56,
    61,
    66,
    67,
    87,
    94,
    97,
    100
   ],
   [
    1,
    4,
    64,
    69,
    74,
    75,
    95,
    102
   ],
   [
    5,
    74,
    76,
    81,
    86,
    96,
    99
   ],
   [
    0,
    3,
    7,
    13,
    82,
    84,
    89,
    94
   ],
   [
    8,
    11,
    15,
    21,
    90,
    92,
    97,
    102
   ],
   [
    1,
    6,
    16,
    19,
    23,
    29,
    98,
    100
   ],
   [
    2,
    4,
    9,
    14,
    24,
    27,
    31,
    37
   ],
   [
    10,
    12,
    17,
    22,
    32,
    35,
    39,
    45
   ],
   [
    18,
    20,
    25,
    30,
    40,
    43,
    47,
    53
   ],
   [
    26,
    28,
    33,
    38,
    48,
    51,
    55,
    61
   ],
   [
    34,
    36,
    41,
    46,
    56,
    59,
    63,
    69
   ],
   [
    42,
    44,
    49,
    54,
    64,
    67,
    71,
    77
   ],
   [
    50,
    52,
    57,
    62,
    72,
    75,
    79,
    85
   ],
   [
    58,
    60,
    65,
    70,
    80,
    83,
    87,
    93
   ],
   [
    66,
    68,
    73,
    78,
    88,
    91,
    95,
    101
   ],
   [
    3,
    18,
    22,
    57,
    61,
    64,
    68
   ],
   [
    7,
    11,
    26,
    30,
    65,
    69,
    72,
    76
   ],
   [
    15,
    19,
    34,
    38,
    73,
    77,
    80,
    84
   ],
   [
    23,
    27,
    42,
    46,
    81,
    85,
    88,
    92
   ],
   [
    31,
    35,
    50,
    54,
    89,
    93,
    96,
    100
   ],
   [
    0,
    4,
    39,
    43,
    58,
    62,
    97,
    101
   ],
   [
    1,
    5,
    8,
    12,
    47,
    51,
    66,
    70
   ],
   [
    9,
    13,
    16,
    20,
    55,
    59,
    74,
    78
   ],
   [
    17,
    21,
    24,
    28,
    63,
    67,
    82,
    86
   ],
   [
    25,
    29,
    32,
    36,
    71,
    75,
    90,
    94
   ],
   [
    33,
    37,
    40,
    44,
    79,
    83,
    98,
    102
   ],
   [
    2,
    6,
    41,
    45,
    48,
    52,
    87,
    91
   ],
   [
    10,
    14,
    49,
    53,
    56,
    60,
    95,
    99
   ]
  ]
 },
 "distance": {
  "d": 7,
  "X": {
   "value": 8,
   "confidence": "upper_bound",
   "witness": [
    5,
    26,
    30,
    40,
    44,
    51,
    54,
    96
   ]
  },
  "Z": {
   "value": 7,
   "confidence": "upper_bound",
   "witness": [
    6,
    34,
    38,
    55,
    59,
    90,
    91
   ]
  }
 },
 "provenance": {
  "authors": [
   "@davidplu"
  ],
  "construction": "Shorten the X-check row space at parent qubit 0 and puncture the Z checks at that qubit, starting from codes/104-30-8.json. Use the first X check containing qubit 0 as pivot, XOR it into every other X check containing that qubit, remove the pivot check, and delete column 0 from both matrices.",
  "references": [
   "arXiv:2607.14091"
  ],
  "date": "2026-09-29",
  "notes": "Derived from the Jong Yeon Lee pair-partition CPM baseline, not an independent discovery of that construction. Literature novelty of the shortened parameters is unverified. The parent entry is codes/104-30-8.json at upstream commit c665b033956000ca1c058de851b8cd25b1ab289b. The initial trusted board comparison found no exact duplicate or WL-equivalent entry; the differing blocklength also rules out equivalence to the parent by a qubit permutation. The cost of saving one physical qubit is a distance bound of 7 rather than 8 and maximum check weight 14 rather than 8. Independent RIS screens at 10,000, 100,000 and 2,000,000 trials per side all returned 7 (seeds 290927, 290928, 290930, pair depth 16, two threads). No exact-distance or literature-novelty claim is made.",
  "model": "GPT-6 (Codex)",
  "origin": "submission",
  "novelty": "unknown"
 },
 "family": "other"
}
