{ "schema_version": "0.4", "name": "[[88,24,7]] halved CPM pair-partition, (J,L)=(3,8), P=22", "code_type": "stabilizer", "n": 88, "k": 24, "checks": { "S": [ { "X": [ 9, 22, 50, 67 ], "Z": [ 11, 34, 61, 84 ] }, { "X": [ 10, 23, 51, 68 ], "Z": [ 10, 33, 60, 83 ] }, { "X": [ 11, 24, 52, 69 ], "Z": [ 9, 32, 59, 82 ] }, { "X": [ 12, 25, 53, 70 ], "Z": [ 8, 31, 58, 81 ] }, { "X": [ 13, 26, 54, 71 ], "Z": [ 7, 30, 57, 80 ] }, { "X": [ 14, 27, 55, 72 ], "Z": [ 6, 29, 56, 79 ] }, { "X": [ 15, 28, 56, 73 ], "Z": [ 5, 28, 55, 78 ] }, { "X": [ 16, 29, 57, 74 ], "Z": [ 4, 27, 54, 77 ] }, { "X": [ 17, 30, 58, 75 ], "Z": [ 3, 26, 53, 76 ] }, { "X": [ 18, 31, 59, 76 ], "Z": [ 2, 25, 52, 75 ] }, { "X": [ 19, 32, 60, 77 ], "Z": [ 1, 24, 51, 74 ] }, { "X": [ 20, 33, 61, 78 ], "Z": [ 0, 23, 50, 73 ] }, { "X": [ 21, 34, 62, 79 ], "Z": [ 21, 22, 49, 72 ] }, { "X": [ 0, 35, 63, 80 ], "Z": [ 20, 43, 48, 71 ] }, { "X": [ 1, 36, 64, 81 ], "Z": [ 19, 42, 47, 70 ] }, { "X": [ 2, 37, 65, 82 ], "Z": [ 18, 41, 46, 69 ] }, { "X": [ 3, 38, 44, 83 ], "Z": [ 17, 40, 45, 68 ] }, { "X": [ 4, 39, 45, 84 ], "Z": [ 16, 39, 44, 67 ] }, { "X": [ 5, 40, 46, 85 ], "Z": [ 15, 38, 65, 66 ] }, { "X": [ 6, 41, 47, 86 ], "Z": [ 14, 37, 64, 87 ] }, { "X": [ 7, 42, 48, 87 ], "Z": [ 13, 36, 63, 86 ] }, { "X": [ 8, 43, 49, 66 ], "Z": [ 12, 35, 62, 85 ] }, { "X": [ 13, 43, 62, 85 ], "Z": [ 16, 42, 63, 74 ] }, { "X": [ 14, 22, 63, 86 ], "Z": [ 15, 41, 62, 73 ] }, { "X": [ 15, 23, 64, 87 ], "Z": [ 14, 40, 61, 72 ] }, { "X": [ 16, 24, 65, 66 ], "Z": [ 13, 39, 60, 71 ] }, { "X": [ 17, 25, 44, 67 ], "Z": [ 12, 38, 59, 70 ] }, { "X": [ 18, 26, 45, 68 ], "Z": [ 11, 37, 58, 69 ] }, { "X": [ 19, 27, 46, 69 ], "Z": [ 10, 36, 57, 68 ] }, { "X": [ 20, 28, 47, 70 ], "Z": [ 9, 35, 56, 67 ] }, { "X": [ 21, 29, 48, 71 ], "Z": [ 8, 34, 55, 66 ] }, { "X": [ 0, 30, 49, 72 ], "Z": [ 7, 33, 54, 87 ] }, { "X": [ 1, 31, 50, 73 ], "Z": [ 6, 32, 53, 86 ] }, { "X": [ 2, 32, 51, 74 ], "Z": [ 5, 31, 52, 85 ] }, { "X": [ 3, 33, 52, 75 ], "Z": [ 4, 30, 51, 84 ] }, { "X": [ 4, 34, 53, 76 ], "Z": [ 3, 29, 50, 83 ] }, { "X": [ 5, 35, 54, 77 ], "Z": [ 2, 28, 49, 82 ] }, { "X": [ 6, 36, 55, 78 ], "Z": [ 1, 27, 48, 81 ] }, { "X": [ 7, 37, 56, 79 ], "Z": [ 0, 26, 47, 80 ] }, { "X": [ 8, 38, 57, 80 ], "Z": [ 21, 25, 46, 79 ] }, { "X": [ 9, 39, 58, 81 ], "Z": [ 20, 24, 45, 78 ] }, { "X": [ 10, 40, 59, 82 ], "Z": [ 19, 23, 44, 77 ] }, { "X": [ 11, 41, 60, 83 ], "Z": [ 18, 22, 65, 76 ] }, { "X": [ 12, 42, 61, 84 ], "Z": [ 17, 43, 64, 75 ] }, { "X": [ 21, 43, 49, 75 ], "Z": [ 5, 40, 59, 80 ] }, { "X": [ 0, 22, 50, 76 ], "Z": [ 4, 39, 58, 79 ] }, { "X": [ 1, 23, 51, 77 ], "Z": [ 3, 38, 57, 78 ] }, { "X": [ 2, 24, 52, 78 ], "Z": [ 2, 37, 56, 77 ] }, { "X": [ 3, 25, 53, 79 ], "Z": [ 1, 36, 55, 76 ] }, { "X": [ 4, 26, 54, 80 ], "Z": [ 0, 35, 54, 75 ] }, { "X": [ 5, 27, 55, 81 ], "Z": [ 21, 34, 53, 74 ] }, { "X": [ 6, 28, 56, 82 ], "Z": [ 20, 33, 52, 73 ] }, { "X": [ 7, 29, 57, 83 ], "Z": [ 19, 32, 51, 72 ] }, { "X": [ 8, 30, 58, 84 ], "Z": [ 18, 31, 50, 71 ] }, { "X": [ 9, 31, 59, 85 ], "Z": [ 17, 30, 49, 70 ] }, { "X": [ 10, 32, 60, 86 ], "Z": [ 16, 29, 48, 69 ] }, { "X": [ 11, 33, 61, 87 ], "Z": [ 15, 28, 47, 68 ] }, { "X": [ 12, 34, 62, 66 ], "Z": [ 14, 27, 46, 67 ] }, { "X": [ 13, 35, 63, 67 ], "Z": [ 13, 26, 45, 66 ] }, { "X": [ 14, 36, 64, 68 ], "Z": [ 12, 25, 44, 87 ] }, { "X": [ 15, 37, 65, 69 ], "Z": [ 11, 24, 65, 86 ] }, { "X": [ 16, 38, 44, 70 ], "Z": [ 10, 23, 64, 85 ] }, { "X": [ 17, 39, 45, 71 ], "Z": [ 9, 22, 63, 84 ] }, { "X": [ 18, 40, 46, 72 ], "Z": [ 8, 43, 62, 83 ] }, { "X": [ 19, 41, 47, 73 ], "Z": [ 7, 42, 61, 82 ] }, { "X": [ 20, 42, 48, 74 ], "Z": [ 6, 41, 60, 81 ] } ] }, "distance": { "d": 7, "P": { "value": 7, "confidence": "upper_bound", "witness": { "X": [ 17, 45 ], "Z": [ 9, 17, 39, 58, 67, 84 ] } } }, "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)=(3,8), lift P=22. Exponent array E (rows a=0..2, columns l=0..7): [[13, 11, 0, 12, 16, 17, 21, 18], [9, 16, 1, 20, 4, 19, 3, 8], [1, 5, 1, 18, 17, 15, 13, 14]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 6], [1, 2], [3, 4], [5, 7]], \"0,2\": [[0, 2], [1, 5], [3, 6], [4, 7]], \"1,2\": [[0, 5], [1, 6], [2, 4], [3, 7]]}. The paper publishes no generators for its halved instances; this code is from a random search over the template. Distance 7 is the lightest Pauli logical found through 1634 random per-qubit symplectic frames x 1,000,000 gf2_fast trials on the symplectic doubling (upper bound). The paper's Table VII lists [[88,24,8]] at this lift, as an exact value; this search did not reach 8, so the entry is 1 short of the published value.", "model": "Claude Fable 5.1", "search_budget": { "candidates_screened": 120908, "ris_trials_per_side": 1634000000, "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 3000 trials per template (Perlmutter job 59705502, 2026-10-12), then 444 frames x 1,000,000 gf2_fast trials (jobs 59731365 to 59731368) and 1190 further frames x 1,000,000 trials with fresh seeds (job 59779389, 2026-10-14). Lightest Pauli logical found: 7." } } }