{"paper":{"title":"New constructions of Hadamard matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ka Hin Leung, Koji Momihara","submitted_at":"2018-09-14T04:53:24Z","abstract_excerpt":"In this paper, we obtain a number of new infinite families of Hadamard matrices. Our constructions are based on four new constructions of difference families with four or eight blocks. By applying the Wallis-Whiteman array or the Kharaghani array to the difference families constructed, we obtain new Hadamard matrices of order $4(uv+1)$ for $u=2$ and $v\\in \\Phi_1\\cup \\Phi_2 \\cup \\Phi_3 \\cup \\Phi_4$; and for $u\\in \\{3,5\\}$ and $v\\in \\Phi_1\\cup \\Phi_2 \\cup \\Phi_3$. Here, $\\Phi_1=\\{q^2:q\\equiv 1\\pmod{4}\\mbox{ is a prime power}\\}$, $\\Phi_2=\\{n^4\\in \\mathbb{N}:n\\equiv 1\\pmod{2}\\} \\cup \\{9n^4\\in \\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05253","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}