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418, 431, 477, 480, 526 ], [ 233, 263, 323, 405, 419, 427, 504, 507, 527 ], [ 254, 287, 310, 334, 393, 420, 452, 480, 528 ], [ 268, 274, 290, 335, 396, 421, 456, 459, 529 ], [ 231, 236, 272, 333, 412, 422, 489, 530, 531 ], [ 273, 289, 304, 350, 389, 423, 460, 490, 531 ], [ 234, 264, 314, 331, 340, 424, 461, 531, 532 ], [ 267, 278, 298, 343, 404, 425, 444, 492, 533 ], [ 218, 240, 285, 339, 421, 426, 451, 523, 534 ], [ 250, 286, 313, 361, 402, 427, 534, 535, 536 ], [ 243, 277, 318, 324, 349, 428, 451, 500, 536 ], [ 234, 291, 307, 352, 413, 429, 438, 506, 537 ], [ 254, 290, 299, 325, 360, 430, 486, 516, 538 ], [ 251, 267, 308, 327, 373, 431, 473, 475, 539 ] ] }, "distance": { "d": 18, "X": { "value": 18, "confidence": "upper_bound", "witness": [ 218, 252, 260, 261, 267, 289, 290, 292, 299, 304, 305, 308, 329, 356, 369, 381, 404, 421 ] }, "Z": { "value": 18, "confidence": "upper_bound", "witness": [ 109, 162, 171, 180, 192, 198, 201, 324, 334, 339, 360, 361, 378, 379, 380, 412, 427, 428 ] } }, "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(108,9) = C9 : C12, base matrices A = [a0|a1], B = [b0|b1] from Table XIII, entries as 0-based indices into Elements(G): a0=[20, 35, 52], a1=[0, 36, 39], b0=[38, 63, 104], b1=[0, 35, 94]. 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). Independent reconstruction from Table XIII + GAP Elements ordering reproduces the published H_X/H_Z bit-for-bit.", "references": [ "arXiv:2607.28795" ], "date": "2026", "notes": "Literature baseline. Paper claims d = 18 (exact, via sQetch + BP+OSD estimators; not certified here). Seeded per issue #377.", "origin": "baseline" }, "family": "lifted-product" }