{"paper":{"title":"Cretan(4t+1) Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jennifer Seberry, N. A. Balonin","submitted_at":"2015-10-20T02:04:53Z","abstract_excerpt":"A $Cretan(4t+1)$ matrix, of order $4t+1$, is an orthogonal matrix whose elements have moduli $\\leq 1$. The only $Cretan(4t+1)$ matrices previously published are for orders 5, 9, 13, 17 and 37. This paper gives infinitely many new $Cretan(4t+1)$ matrices constructed using $regular~Hadamard$ matrices, $SBIBD(4t+1,k,\\lambda)$, weighing matrices, generalized Hadamard matrices and the Kronecker product. We introduce an inequality for the radius and give a construction for a Cretan matrix for every order $n \\geq 3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05736","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"}