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}, "provenance": { "authors": [ "@mathysrennela" ], "construction": "Lifted product over Z_t x Z_2 (|G| = 2t). Protograph A (3x4), B (3x4) from arXiv:2606.24808 Table 1 (R3EliteP02, an SCE-search elite), x-exponents reduced modulo the family parameter t=14 to fit the n<=700 cap: n = (nA*nB + mA*mB)*|G| = 25*28 = 700. A entries act by the left regular representation, B entries by the right regular representation (via inverse); HX = [A~ (x) I_4 | I_3 (x) B~^T], HZ = [I_4 (x) B~ | A~^T (x) I_3] (protograph-level Kronecker, expanded block transposes in HZ). The paper reports [[1500,76,<=20]] at t=30; this is the same protograph at a smaller lift. Distance is a witness-backed upper bound (randomized information-set search).", "origin": "submission", "date": "2026-09-14", "model": "GLM 5.3 Flash", "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=14), 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.", "references": [ "arXiv:2606.24808" ] }, "family": "lifted-product" }