{
 "schema_version": "0.4",
 "name": "[[120,27,12]] halved CPM pair-partition, (J,L)=(4,10), P=24",
 "code_type": "stabilizer",
 "n": 120,
 "k": 27,
 "checks": {
  "S": [
   {
    "X": [
     5,
     35,
     67,
     85,
     111
    ],
    "Z": [
     9,
     44,
     59,
     80,
     110
    ]
   },
   {
    "X": [
     6,
     36,
     68,
     86,
     112
    ],
    "Z": [
     8,
     43,
     58,
     79,
     109
    ]
   },
   {
    "X": [
     7,
     37,
     69,
     87,
     113
    ],
    "Z": [
     7,
     42,
     57,
     78,
     108
    ]
   },
   {
    "X": [
     8,
     38,
     70,
     88,
     114
    ],
    "Z": [
     6,
     41,
     56,
     77,
     107
    ]
   },
   {
    "X": [
     9,
     39,
     71,
     89,
     115
    ],
    "Z": [
     5,
     40,
     55,
     76,
     106
    ]
   },
   {
    "X": [
     10,
     40,
     48,
     90,
     116
    ],
    "Z": [
     4,
     39,
     54,
     75,
     105
    ]
   },
   {
    "X": [
     11,
     41,
     49,
     91,
     117
    ],
    "Z": [
     3,
     38,
     53,
     74,
     104
    ]
   },
   {
    "X": [
     12,
     42,
     50,
     92,
     118
    ],
    "Z": [
     2,
     37,
     52,
     73,
     103
    ]
   },
   {
    "X": [
     13,
     43,
     51,
     93,
     119
    ],
    "Z": [
     1,
     36,
     51,
     72,
     102
    ]
   },
   {
    "X": [
     14,
     44,
     52,
     94,
     96
    ],
    "Z": [
     0,
     35,
     50,
     95,
     101
    ]
   },
   {
    "X": [
     15,
     45,
     53,
     95,
     97
    ],
    "Z": [
     23,
     34,
     49,
     94,
     100
    ]
   },
   {
    "X": [
     16,
     46,
     54,
     72,
     98
    ],
    "Z": [
     22,
     33,
     48,
     93,
     99
    ]
   },
   {
    "X": [
     17,
     47,
     55,
     73,
     99
    ],
    "Z": [
     21,
     32,
     71,
     92,
     98
    ]
   },
   {
    "X": [
     18,
     24,
     56,
     74,
     100
    ],
    "Z": [
     20,
     31,
     70,
     91,
     97
    ]
   },
   {
    "X": [
     19,
     25,
     57,
     75,
     101
    ],
    "Z": [
     19,
     30,
     69,
     90,
     96
    ]
   },
   {
    "X": [
     20,
     26,
     58,
     76,
     102
    ],
    "Z": [
     18,
     29,
     68,
     89,
     119
    ]
   },
   {
    "X": [
     21,
     27,
     59,
     77,
     103
    ],
    "Z": [
     17,
     28,
     67,
     88,
     118
    ]
   },
   {
    "X": [
     22,
     28,
     60,
     78,
     104
    ],
    "Z": [
     16,
     27,
     66,
     87,
     117
    ]
   },
   {
    "X": [
     23,
     29,
     61,
     79,
     105
    ],
    "Z": [
     15,
     26,
     65,
     86,
     116
    ]
   },
   {
    "X": [
     0,
     30,
     62,
     80,
     106
    ],
    "Z": [
     14,
     25,
     64,
     85,
     115
    ]
   },
   {
    "X": [
     1,
     31,
     63,
     81,
     107
    ],
    "Z": [
     13,
     24,
     63,
     84,
     114
    ]
   },
   {
    "X": [
     2,
     32,
     64,
     82,
     108
    ],
    "Z": [
     12,
     47,
     62,
     83,
     113
    ]
   },
   {
    "X": [
     3,
     33,
     65,
     83,
     109
    ],
    "Z": [
     11,
     46,
     61,
     82,
     112
    ]
   },
   {
    "X": [
     4,
     34,
     66,
     84,
     110
    ],
    "Z": [
     10,
     45,
     60,
     81,
     111
    ]
   },
   {
    "X": [
     7,
     40,
     55,
     87,
     100
    ],
    "Z": [
     1,
     45,
     63,
     87,
     104
    ]
   },
   {
    "X": [
     8,
     41,
     56,
     88,
     101
    ],
    "Z": [
     0,
     44,
     62,
     86,
     103
    ]
   },
   {
    "X": [
     9,
     42,
     57,
     89,
     102
    ],
    "Z": [
     23,
     43,
     61,
     85,
     102
    ]
   },
   {
    "X": [
     10,
     43,
     58,
     90,
     103
    ],
    "Z": [
     22,
     42,
     60,
     84,
     101
    ]
   },
   {
    "X": [
     11,
     44,
     59,
     91,
     104
    ],
    "Z": [
     21,
     41,
     59,
     83,
     100
    ]
   },
   {
    "X": [
     12,
     45,
     60,
     92,
     105
    ],
    "Z": [
     20,
     40,
     58,
     82,
     99
    ]
   },
   {
    "X": [
     13,
     46,
     61,
     93,
     106
    ],
    "Z": [
     19,
     39,
     57,
     81,
     98
    ]
   },
   {
    "X": [
     14,
     47,
     62,
     94,
     107
    ],
    "Z": [
     18,
     38,
     56,
     80,
     97
    ]
   },
   {
    "X": [
     15,
     24,
     63,
     95,
     108
    ],
    "Z": [
     17,
     37,
     55,
     79,
     96
    ]
   },
   {
    "X": [
     16,
     25,
     64,
     72,
     109
    ],
    "Z": [
     16,
     36,
     54,
     78,
     119
    ]
   },
   {
    "X": [
     17,
     26,
     65,
     73,
     110
    ],
    "Z": [
     15,
     35,
     53,
     77,
     118
    ]
   },
   {
    "X": [
     18,
     27,
     66,
     74,
     111
    ],
    "Z": [
     14,
     34,
     52,
     76,
     117
    ]
   },
   {
    "X": [
     19,
     28,
     67,
     75,
     112
    ],
    "Z": [
     13,
     33,
     51,
     75,
     116
    ]
   },
   {
    "X": [
     20,
     29,
     68,
     76,
     113
    ],
    "Z": [
     12,
     32,
     50,
     74,
     115
    ]
   },
   {
    "X": [
     21,
     30,
     69,
     77,
     114
    ],
    "Z": [
     11,
     31,
     49,
     73,
     114
    ]
   },
   {
    "X": [
     22,
     31,
     70,
     78,
     115
    ],
    "Z": [
     10,
     30,
     48,
     72,
     113
    ]
   },
   {
    "X": [
     23,
     32,
     71,
     79,
     116
    ],
    "Z": [
     9,
     29,
     71,
     95,
     112
    ]
   },
   {
    "X": [
     0,
     33,
     48,
     80,
     117
    ],
    "Z": [
     8,
     28,
     70,
     94,
     111
    ]
   },
   {
    "X": [
     1,
     34,
     49,
     81,
     118
    ],
    "Z": [
     7,
     27,
     69,
     93,
     110
    ]
   },
   {
    "X": [
     2,
     35,
     50,
     82,
     119
    ],
    "Z": [
     6,
     26,
     68,
     92,
     109
    ]
   },
   {
    "X": [
     3,
     36,
     51,
     83,
     96
    ],
    "Z": [
     5,
     25,
     67,
     91,
     108
    ]
   },
   {
    "X": [
     4,
     37,
     52,
     84,
     97
    ],
    "Z": [
     4,
     24,
     66,
     90,
     107
    ]
   },
   {
    "X": [
     5,
     38,
     53,
     85,
     98
    ],
    "Z": [
     3,
     47,
     65,
     89,
     106
    ]
   },
   {
    "X": [
     6,
     39,
     54,
     86,
     99
    ],
    "Z": [
     2,
     46,
     64,
     88,
     105
    ]
   },
   {
    "X": [
     6,
     40,
     61,
     82,
     107
    ],
    "Z": [
     9,
     35,
     66,
     84,
     111
    ]
   },
   {
    "X": [
     7,
     41,
     62,
     83,
     108
    ],
    "Z": [
     8,
     34,
     65,
     83,
     110
    ]
   },
   {
    "X": [
     8,
     42,
     63,
     84,
     109
    ],
    "Z": [
     7,
     33,
     64,
     82,
     109
    ]
   },
   {
    "X": [
     9,
     43,
     64,
     85,
     110
    ],
    "Z": [
     6,
     32,
     63,
     81,
     108
    ]
   },
   {
    "X": [
     10,
     44,
     65,
     86,
     111
    ],
    "Z": [
     5,
     31,
     62,
     80,
     107
    ]
   },
   {
    "X": [
     11,
     45,
     66,
     87,
     112
    ],
    "Z": [
     4,
     30,
     61,
     79,
     106
    ]
   },
   {
    "X": [
     12,
     46,
     67,
     88,
     113
    ],
    "Z": [
     3,
     29,
     60,
     78,
     105
    ]
   },
   {
    "X": [
     13,
     47,
     68,
     89,
     114
    ],
    "Z": [
     2,
     28,
     59,
     77,
     104
    ]
   },
   {
    "X": [
     14,
     24,
     69,
     90,
     115
    ],
    "Z": [
     1,
     27,
     58,
     76,
     103
    ]
   },
   {
    "X": [
     15,
     25,
     70,
     91,
     116
    ],
    "Z": [
     0,
     26,
     57,
     75,
     102
    ]
   },
   {
    "X": [
     16,
     26,
     71,
     92,
     117
    ],
    "Z": [
     23,
     25,
     56,
     74,
     101
    ]
   },
   {
    "X": [
     17,
     27,
     48,
     93,
     118
    ],
    "Z": [
     22,
     24,
     55,
     73,
     100
    ]
   },
   {
    "X": [
     18,
     28,
     49,
     94,
     119
    ],
    "Z": [
     21,
     47,
     54,
     72,
     99
    ]
   },
   {
    "X": [
     19,
     29,
     50,
     95,
     96
    ],
    "Z": [
     20,
     46,
     53,
     95,
     98
    ]
   },
   {
    "X": [
     20,
     30,
     51,
     72,
     97
    ],
    "Z": [
     19,
     45,
     52,
     94,
     97
    ]
   },
   {
    "X": [
     21,
     31,
     52,
     73,
     98
    ],
    "Z": [
     18,
     44,
     51,
     93,
     96
    ]
   },
   {
    "X": [
     22,
     32,
     53,
     74,
     99
    ],
    "Z": [
     17,
     43,
     50,
     92,
     119
    ]
   },
   {
    "X": [
     23,
     33,
     54,
     75,
     100
    ],
    "Z": [
     16,
     42,
     49,
     91,
     118
    ]
   },
   {
    "X": [
     0,
     34,
     55,
     76,
     101
    ],
    "Z": [
     15,
     41,
     48,
     90,
     117
    ]
   },
   {
    "X": [
     1,
     35,
     56,
     77,
     102
    ],
    "Z": [
     14,
     40,
     71,
     89,
     116
    ]
   },
   {
    "X": [
     2,
     36,
     57,
     78,
     103
    ],
    "Z": [
     13,
     39,
     70,
     88,
     115
    ]
   },
   {
    "X": [
     3,
     37,
     58,
     79,
     104
    ],
    "Z": [
     12,
     38,
     69,
     87,
     114
    ]
   },
   {
    "X": [
     4,
     38,
     59,
     80,
     105
    ],
    "Z": [
     11,
     37,
     68,
     86,
     113
    ]
   },
   {
    "X": [
     5,
     39,
     60,
     81,
     106
    ],
    "Z": [
     10,
     36,
     67,
     85,
     112
    ]
   },
   {
    "X": [
     11,
     39,
     58,
     84,
     114
    ],
    "Z": [
     3,
     36,
     61,
     90,
     105
    ]
   },
   {
    "X": [
     12,
     40,
     59,
     85,
     115
    ],
    "Z": [
     2,
     35,
     60,
     89,
     104
    ]
   },
   {
    "X": [
     13,
     41,
     60,
     86,
     116
    ],
    "Z": [
     1,
     34,
     59,
     88,
     103
    ]
   },
   {
    "X": [
     14,
     42,
     61,
     87,
     117
    ],
    "Z": [
     0,
     33,
     58,
     87,
     102
    ]
   },
   {
    "X": [
     15,
     43,
     62,
     88,
     118
    ],
    "Z": [
     23,
     32,
     57,
     86,
     101
    ]
   },
   {
    "X": [
     16,
     44,
     63,
     89,
     119
    ],
    "Z": [
     22,
     31,
     56,
     85,
     100
    ]
   },
   {
    "X": [
     17,
     45,
     64,
     90,
     96
    ],
    "Z": [
     21,
     30,
     55,
     84,
     99
    ]
   },
   {
    "X": [
     18,
     46,
     65,
     91,
     97
    ],
    "Z": [
     20,
     29,
     54,
     83,
     98
    ]
   },
   {
    "X": [
     19,
     47,
     66,
     92,
     98
    ],
    "Z": [
     19,
     28,
     53,
     82,
     97
    ]
   },
   {
    "X": [
     20,
     24,
     67,
     93,
     99
    ],
    "Z": [
     18,
     27,
     52,
     81,
     96
    ]
   },
   {
    "X": [
     21,
     25,
     68,
     94,
     100
    ],
    "Z": [
     17,
     26,
     51,
     80,
     119
    ]
   },
   {
    "X": [
     22,
     26,
     69,
     95,
     101
    ],
    "Z": [
     16,
     25,
     50,
     79,
     118
    ]
   },
   {
    "X": [
     23,
     27,
     70,
     72,
     102
    ],
    "Z": [
     15,
     24,
     49,
     78,
     117
    ]
   },
   {
    "X": [
     0,
     28,
     71,
     73,
     103
    ],
    "Z": [
     14,
     47,
     48,
     77,
     116
    ]
   },
   {
    "X": [
     1,
     29,
     48,
     74,
     104
    ],
    "Z": [
     13,
     46,
     71,
     76,
     115
    ]
   },
   {
    "X": [
     2,
     30,
     49,
     75,
     105
    ],
    "Z": [
     12,
     45,
     70,
     75,
     114
    ]
   },
   {
    "X": [
     3,
     31,
     50,
     76,
     106
    ],
    "Z": [
     11,
     44,
     69,
     74,
     113
    ]
   },
   {
    "X": [
     4,
     32,
     51,
     77,
     107
    ],
    "Z": [
     10,
     43,
     68,
     73,
     112
    ]
   },
   {
    "X": [
     5,
     33,
     52,
     78,
     108
    ],
    "Z": [
     9,
     42,
     67,
     72,
     111
    ]
   },
   {
    "X": [
     6,
     34,
     53,
     79,
     109
    ],
    "Z": [
     8,
     41,
     66,
     95,
     110
    ]
   },
   {
    "X": [
     7,
     35,
     54,
     80,
     110
    ],
    "Z": [
     7,
     40,
     65,
     94,
     109
    ]
   },
   {
    "X": [
     8,
     36,
     55,
     81,
     111
    ],
    "Z": [
     6,
     39,
     64,
     93,
     108
    ]
   },
   {
    "X": [
     9,
     37,
     56,
     82,
     112
    ],
    "Z": [
     5,
     38,
     63,
     92,
     107
    ]
   },
   {
    "X": [
     10,
     38,
     57,
     83,
     113
    ],
    "Z": [
     4,
     37,
     62,
     91,
     106
    ]
   }
  ]
 },
 "distance": {
  "d": 12,
  "P": {
   "value": 12,
   "confidence": "upper_bound",
   "witness": {
    "X": [
     1,
     7,
     13,
     19,
     28,
     34,
     40,
     46,
     76,
     82,
     88,
     94
    ],
    "Z": [
     1,
     7,
     13,
     19
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "origin": "submission",
  "construction": "search",
  "date": "2026-10-15",
  "references": [
   "arXiv:2609.30069"
  ],
  "notes": "Halved CPM pair-partition code of arXiv:2609.30069 (Definition 1, reversing fold of Proposition 4) at (J,L)=(4,10), lift P=24. Exponent array E (rows a=0..3, columns l=0..9): [[19, 9, 13, 20, 5, 11, 11, 8, 9, 14], [17, 1, 8, 21, 17, 15, 9, 15, 20, 8], [18, 9, 8, 11, 11, 18, 14, 12, 13, 15], [13, 3, 9, 12, 14, 13, 12, 18, 6, 9]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 4], [1, 6], [2, 9], [3, 5], [7, 8]], \"0,2\": [[0, 3], [1, 9], [2, 8], [4, 6], [5, 7]], \"0,3\": [[0, 1], [2, 5], [3, 6], [4, 8], [7, 9]], \"1,2\": [[0, 5], [1, 2], [3, 7], [4, 8], [6, 9]], \"1,3\": [[0, 2], [1, 9], [3, 4], [5, 8], [6, 7]], \"2,3\": [[0, 9], [1, 8], [2, 3], [4, 7], [5, 6]]}. The paper publishes no generators for its halved instances; this code is from a random search over the template. Distance 12 is the lightest Pauli logical found through 850 random per-qubit symplectic frames x 1,000,000 gf2_fast trials on the symplectic doubling (upper bound). The paper's Table VII has no row at P = 24 for the (4,10) family (its nearest lifts are 18, 20, 22, 26, 28, 30), so there is no published value at this (n, k).",
  "model": "Claude Fable 5.1",
  "search_budget": {
   "candidates_screened": 336865,
   "ris_trials_per_side": 850000000,
   "tool": "halved_pp.py templates; verify/heuristic_distance.py Pauli RIS; gf2_fast on the symplectic doubling under random per-qubit symplectic frames (frame_screen.py)",
   "notes": "Pauli-weight RIS screen at 2000 trials per template (Perlmutter job 59705375, 2026-10-12), then 240 frames x 1,000,000 gf2_fast trials (jobs 59731365 to 59731368) and 610 further frames x 1,000,000 trials with fresh seeds (job 59779389, 2026-10-14). Lightest Pauli logical found: 12."
  }
 }
}