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276, 283, 310, 366, 426, 480 ], [ 250, 277, 282, 311, 367, 427, 481 ], [ 253, 278, 285, 312, 368, 428, 482 ], [ 252, 279, 284, 313, 369, 429, 483 ], [ 255, 260, 287, 314, 370, 430, 484 ], [ 254, 261, 286, 315, 371, 431, 485 ] ] }, "distance": { "d": 12, "X": { "value": 12, "confidence": "upper_bound", "witness": [ 1, 11, 43, 53, 246, 256, 288, 298, 348, 358, 468, 478 ] }, "Z": { "value": 12, "confidence": "upper_bound", "witness": [ 29, 39, 104, 107, 108, 114, 117, 118, 186, 196, 264, 274 ] } }, "provenance": { "authors": [ "@mathysrennela" ], "construction": "Lifted product over Z_t x Z_2 (|G|=20), protograph A (3x4), B (3x4) taken from arXiv:2606.24808 Table 1 (R3EliteP02, an SCE search elite), with the paper's exponents reduced modulo the family parameter t=10 to fit the board's n<=700 cap (n = (nA*nB + mA*mB)*|G| = 25*20 = 500). Entries of A act by left regular representation, entries of B by right regular representation (via inverse), HX = [A~(x)I | I(x)B~^T], HZ = [I(x)B~^T-blocks | A~^T-blocks]. Paper reports [[1500,76,<=pd]] at t=30; this is the same protograph at a smaller lift. Distance is an upper bound from the kit's randomized witness search.", "references": [ "arXiv:2606.24808" ], "date": "2026-09-14", "notes": "Construction family and protograph published in arXiv:2606.24808 (R3EliteP02 at t=30, reported [[1500,76,<=20]]); this entry is the same protograph at a new, smaller lift (t=10), a parameter point the paper does not tabulate; literature novelty of the parameter set unverified. Board dedup gate-checked: not an exact or WL-equivalent duplicate of any existing entry.", "model": "GLM 5.3 Flash", "origin": "submission" }, "family": "lifted-product" }