{ "schema_version": "0.1", "name": "[[112,12,10]] CLP code (arXiv:2610.12782 Table I, weight 7)", "code_type": "CSS", "n": 112, "k": 12, "checks": { "X": [ [ 0, 8, 13, 56, 74, 84, 99 ], [ 1, 7, 10, 57, 77, 85, 100 ], [ 2, 12, 17, 58, 78, 86, 103 ], [ 3, 5, 16, 59, 79, 87, 94 ], [ 2, 4, 15, 60, 80, 88, 97 ], [ 5, 11, 14, 61, 81, 89, 104 ], [ 6, 16, 21, 56, 62, 90, 107 ], [ 7, 9, 20, 63, 82, 91, 98 ], [ 6, 8, 19, 64, 83, 92, 101 ], [ 9, 15, 18, 57, 65, 93, 108 ], [ 10, 20, 25, 58, 66, 94, 110 ], [ 11, 13, 24, 59, 67, 95, 102 ], [ 10, 12, 23, 60, 68, 96, 105 ], [ 13, 19, 22, 61, 69, 97, 111 ], [ 1, 14, 24, 62, 70, 87, 98 ], [ 15, 17, 27, 63, 71, 99, 106 ], [ 14, 16, 26, 64, 72, 100, 109 ], [ 0, 17, 23, 65, 73, 88, 101 ], [ 5, 18, 27, 66, 74, 91, 102 ], [ 4, 19, 21, 67, 75, 84, 103 ], [ 3, 18, 20, 68, 76, 85, 104 ], [ 2, 21, 26, 69, 77, 92, 105 ], [ 4, 9, 22, 70, 78, 95, 106 ], [ 8, 23, 25, 71, 79, 86, 107 ], [ 7, 22, 24, 72, 80, 89, 108 ], [ 3, 6, 25, 73, 81, 96, 109 ], [ 1, 12, 26, 75, 82, 90, 110 ], [ 0, 11, 27, 76, 83, 93, 111 ], [ 28, 36, 41, 56, 75, 91, 103 ], [ 29, 35, 38, 57, 76, 92, 104 ], [ 30, 40, 45, 58, 79, 95, 107 ], [ 31, 33, 44, 59, 70, 86, 98 ], [ 30, 32, 43, 60, 73, 89, 101 ], [ 33, 39, 42, 61, 80, 96, 108 ], [ 34, 44, 49, 62, 82, 99, 110 ], [ 35, 37, 48, 63, 74, 90, 102 ], [ 34, 36, 47, 64, 77, 93, 105 ], [ 37, 43, 46, 65, 83, 100, 111 ], [ 38, 48, 53, 59, 66, 87, 103 ], [ 39, 41, 52, 67, 78, 94, 106 ], [ 38, 40, 51, 68, 81, 97, 109 ], [ 41, 47, 50, 60, 69, 88, 104 ], [ 29, 42, 52, 63, 70, 91, 107 ], [ 43, 45, 55, 56, 71, 84, 98 ], [ 42, 44, 54, 57, 72, 85, 101 ], [ 28, 45, 51, 64, 73, 92, 108 ], [ 33, 46, 55, 67, 74, 95, 110 ], [ 32, 47, 49, 58, 75, 86, 102 ], [ 31, 46, 48, 61, 76, 89, 105 ], [ 30, 49, 54, 68, 77, 96, 111 ], [ 32, 37, 50, 71, 78, 87, 99 ], [ 36, 51, 53, 62, 79, 90, 106 ], [ 35, 50, 52, 65, 80, 93, 109 ], [ 31, 34, 53, 72, 81, 88, 100 ], [ 29, 40, 54, 66, 82, 84, 94 ], [ 28, 39, 55, 69, 83, 85, 97 ] ], "Z": [ [ 0, 6, 28, 43, 56, 73, 83 ], [ 1, 9, 29, 44, 57, 70, 82 ], [ 2, 10, 30, 47, 58, 60, 77 ], [ 3, 11, 31, 38, 59, 76, 81 ], [ 4, 12, 32, 41, 60, 75, 78 ], [ 5, 13, 33, 48, 59, 61, 74 ], [ 6, 14, 34, 51, 62, 64, 81 ], [ 7, 15, 35, 42, 57, 63, 80 ], [ 8, 16, 36, 45, 56, 64, 79 ], [ 9, 17, 37, 52, 63, 65, 78 ], [ 10, 18, 38, 54, 57, 66, 68 ], [ 11, 19, 39, 46, 61, 67, 83 ], [ 12, 20, 40, 49, 58, 68, 82 ], [ 13, 21, 41, 55, 56, 67, 69 ], [ 14, 22, 31, 42, 61, 70, 72 ], [ 15, 23, 43, 50, 60, 65, 71 ], [ 16, 24, 44, 53, 59, 62, 72 ], [ 17, 25, 32, 45, 58, 71, 73 ], [ 0, 18, 35, 46, 65, 74, 76 ], [ 19, 26, 28, 47, 64, 69, 75 ], [ 20, 27, 29, 48, 63, 66, 76 ], [ 1, 21, 36, 49, 62, 75, 77 ], [ 2, 22, 39, 50, 69, 78, 80 ], [ 3, 23, 30, 51, 68, 73, 79 ], [ 4, 24, 33, 52, 67, 70, 80 ], [ 5, 25, 40, 53, 66, 79, 81 ], [ 7, 26, 34, 54, 72, 77, 82 ], [ 8, 27, 37, 55, 71, 74, 83 ], [ 0, 19, 43, 54, 84, 101, 111 ], [ 1, 20, 44, 55, 85, 98, 110 ], [ 2, 23, 31, 47, 86, 88, 105 ], [ 3, 14, 38, 50, 87, 104, 109 ], [ 4, 17, 41, 53, 88, 103, 106 ], [ 5, 24, 32, 48, 87, 89, 102 ], [ 6, 26, 35, 51, 90, 92, 109 ], [ 7, 18, 28, 42, 85, 91, 108 ], [ 8, 21, 29, 45, 84, 92, 107 ], [ 9, 27, 36, 52, 91, 93, 106 ], [ 3, 10, 39, 54, 85, 94, 96 ], [ 11, 22, 30, 46, 89, 95, 111 ], [ 12, 25, 33, 49, 86, 96, 110 ], [ 4, 13, 40, 55, 84, 95, 97 ], [ 7, 14, 31, 43, 89, 98, 100 ], [ 0, 15, 34, 50, 88, 93, 99 ], [ 1, 16, 37, 53, 87, 90, 100 ], [ 8, 17, 32, 44, 86, 99, 101 ], [ 11, 18, 35, 47, 93, 102, 104 ], [ 2, 19, 28, 38, 92, 97, 103 ], [ 5, 20, 29, 41, 91, 94, 104 ], [ 12, 21, 36, 48, 90, 103, 105 ], [ 15, 22, 39, 51, 97, 106, 108 ], [ 6, 23, 30, 42, 96, 101, 107 ], [ 9, 24, 33, 45, 95, 98, 108 ], [ 16, 25, 40, 52, 94, 107, 109 ], [ 10, 26, 34, 46, 100, 105, 110 ], [ 13, 27, 37, 49, 99, 102, 111 ] ] }, "distance": { "d": 10, "X": { "value": 10, "confidence": "upper_bound", "witness": [ 6, 26, 28, 34, 85, 88, 96, 103, 105, 110 ] }, "Z": { "value": 10, "confidence": "upper_bound", "witness": [ 57, 64, 68, 73, 76, 77, 93, 101, 105, 109 ] } }, "provenance": { "authors": [ "Rajpurohit, Rajendra Prasad", "Lalitha, V.", "Garani, Shayan Srinivasa", "@MathysRennela" ], "construction": "Coset lifted product (CLP) code of arXiv:2610.12782, Definition III.1, 1x1 over 2x2 layout: a protograph A over F_2[G] acting by the LEFT coset action of G on the cosets G/H, and a protograph B over F_2[N_G(H)] acting by the RIGHT coset action of the normaliser on the same cosets. G = SmallGroup(336,188), H = (non-normal, core free), m = [G:H], n = 4m = 112. Elements are named by the polycyclic generating sequence f_1,...,f_r of SmallGroup(336,188), as in the paper's Appendix A. CSS commutation is automatic (L(g) and R(n) commute for every g in G and n in N_G(H), so each block of H_X H_Z^T is L R + R L = 0 over F_2); no search for it is needed. n, k and the check weight 7 reproduce the paper's Table I exactly. Literature baseline seeded from the published parameters: this entry is a REPRODUCTION built from the paper's printed data, not a new construction and not a new parameter set. The paper certifies d = 10 by integer program; this entry carries witness-backed upper bounds from our own randomized GF(2) search, which is a weaker claim.", "references": [ "arXiv:2610.12782", "arXiv:2606.17268" ], "date": "2026-10-12", "notes": "Literature baseline: a reproduction of the published parameters in arXiv:2610.12782 (Table I), not a new construction and not a new parameter set. The group, subgroup and protographs are the paper's Appendix A data, rebuilt from GAP SmallGroup(l,i); n, k and the check weight reproduce the paper exactly. Reproduced by Space Bunny Alpha 1.0. The distance here is a witness-backed upper bound from our own randomized GF(2) search, a weaker claim than the paper's integer-program certification. See the accompanying note for the full reproduction recipe.", "origin": "baseline", "novelty": "known_parameters", "model": "Space Bunny Alpha 1.0" }, "family": "2bga-coset" }