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419, 477 ], [ 215, 239, 242, 310, 370, 378, 408, 474, 478 ], [ 213, 216, 283, 311, 336, 379, 412, 421, 479 ], [ 217, 250, 291, 340, 380, 386, 403, 410, 480 ], [ 218, 266, 287, 357, 381, 398, 423, 481, 483 ], [ 219, 228, 251, 359, 364, 382, 443, 482, 491 ], [ 220, 247, 250, 344, 376, 383, 427, 483, 497 ], [ 218, 221, 248, 315, 377, 384, 414, 445, 484 ], [ 201, 222, 294, 381, 385, 390, 426, 429, 485 ], [ 223, 259, 273, 349, 386, 391, 416, 447, 486 ], [ 210, 226, 260, 332, 372, 387, 420, 433, 487 ], [ 227, 256, 259, 320, 382, 388, 418, 486, 488 ], [ 224, 225, 228, 321, 353, 389, 422, 435, 489 ], [ 203, 229, 297, 357, 390, 394, 409, 420, 490 ], [ 230, 232, 280, 358, 373, 391, 424, 437, 491 ], [ 232, 235, 265, 327, 387, 392, 426, 462, 492 ], [ 205, 236, 298, 391, 393, 396, 442, 445, 493 ], [ 206, 237, 285, 366, 394, 397, 428, 464, 494 ], [ 238, 241, 244, 335, 369, 395, 436, 452, 495 ], [ 209, 245, 299, 373, 396, 398, 419, 434, 496 ], [ 200, 246, 290, 374, 385, 397, 438, 454, 497 ], [ 214, 254, 293, 380, 398, 399, 444, 478, 498 ], [ 202, 263, 296, 386, 393, 399, 455, 470, 499 ] ] }, "distance": { "d": 16, "X": { "value": 16, "confidence": "upper_bound", "witness": [ 211, 218, 239, 243, 261, 269, 274, 287, 295, 314, 322, 323, 352, 368, 377, 378 ] }, "Z": { "value": 16, "confidence": "upper_bound", "witness": [ 6, 45, 86, 94, 204, 206, 211, 213, 229, 241, 242, 248, 257, 276, 289, 293 ] } }, "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(100,9) = C5 : C20, base matrices A = [a0|a1], B = [b0|b1] from Table XIII, entries as 0-based indices into Elements(G): a0=[19, 84, 87], a1=[0, 75, 78], b0=[39, 45, 71], b1=[0, 7, 77]. 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 = 16 (exact, via sQetch + BP+OSD estimators; not certified here). Seeded per issue #377.", "origin": "baseline" }, "family": "lifted-product" }