{"paper":{"title":"Orderly generation of Butson Hadamard matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"F. Sz\\\"oll\\H{o}si, P.H.J. Lampio, P. \\\"Osterg{\\aa}rd","submitted_at":"2017-07-07T17:58:29Z","abstract_excerpt":"In this paper Butson-type complex Hadamard matrices $\\mathrm{BH}(n,q)$ of order $n$ and complexity $q$ are classified for small parameters by computer-aided methods. Our main results include the enumeration of $\\mathrm{BH}(21,3)$, $\\mathrm{BH}(16,4)$, and $\\mathrm{BH}(14,6)$ matrices. There are exactly $72$, 1786763, and $167776$ such matrices, up to monomial equivalence. Additionally, we show an example of a $\\mathrm{BH}(14,10)$ matrix for the first time, and show the nonexistence of $\\mathrm{BH}(8,15)$, $\\mathrm{BH}(11,q)$ for $q\\in\\{10,12,14,15\\}$, and $\\mathrm{BH}(13,10)$ matrices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02287","kind":"arxiv","version":1},"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"}