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], [ 125, 167, 176, 188, 205, 213, 251, 257, 290 ], [ 121, 163, 179, 191, 206, 210, 247, 253, 293 ], [ 120, 162, 178, 190, 207, 211, 250, 256, 288 ], [ 123, 165, 174, 186, 208, 215, 246, 252, 291 ], [ 122, 164, 175, 187, 209, 214, 248, 254, 289 ] ] }, "distance": { "d": 14, "X": { "value": 14, "confidence": "upper_bound", "witness": [ 1, 4, 19, 22, 23, 26, 40, 50, 62, 69, 76, 86, 114, 115 ] }, "Z": { "value": 14, "confidence": "upper_bound", "witness": [ 11, 32, 33, 36, 49, 56, 120, 134, 139, 140, 142, 145, 170, 175 ] } }, "provenance": { "authors": [ "Bhardwaj, Aditya", "Ma, Muzhou", "Meister, Nadine", "King, Robbie", "Bluvstein, Dolev", "Preskill, John", "Cain, Madelyn", "Xu, Qian", "Huang, Hsin-Yuan" ], "construction": "Mitten code (arXiv:2607.28795, Definition 4): lifted product LP(A,B) over F2[G], G = GAP SmallGroup(60,11) = C10 x S3, base matrices A = [a0|a1], B = [b0|b1] from Table XIII, entries as 0-based indices into Elements(G): a0=[38, 51, 54], a1=[0, 6, 45], b0=[25, 33, 48], b1=[0, 16, 58]. Block form H_X = [[L(a0),0,L(a1),0,R(b0*)],[0,L(a0),0,L(a1),R(b1*)]], H_Z = [[R(b0),R(b1),0,0,L(a0*)],[0,0,R(b0),R(b1),L(a1*)]] with L(g)b(h)=b(gh), R(g)b(h)=b(h g^-1) and * the g->g^-1 involution (paper Definition 8). Check matrices taken from the authors' repository (github.com/a7b/yarn @ 82fb695a1e40, processor_codes/mitten). NOTE: for this code the Table XIII element indices correspond to a different (undocumented) ordering of Elements(G) than current GAP SmallGroup output, so the authors' published matrices are used verbatim; n, k, check weight 9 and the canonical logical operator weights of Table I were all verified against the paper.", "references": [ "arXiv:2607.28795" ], "date": "2026", "notes": "Literature baseline. Paper claims d = 14 (exact, via sQetch + BP+OSD estimators; not certified here). Seeded per issue #377.", "origin": "baseline" }, "family": "lifted-product" }