{"paper":{"title":"The Propus Construction for Symmetric Hadamard 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":"2015-12-06T03:46:40Z","abstract_excerpt":"\\textit{Propus} (which means twins) is a construction method for orthogonal $\\pm 1$ matrices based on a variation of the Williamson array called the \\textit{propus array}\n  \\[ \\begin{matrix*}[r]\n  A& B & B & D\n  B& D & -A &-B\n  B& -A & -D & B\n  D& -B & B &-A.\n  \\end{matrix*} \\]\n  This construction designed to find symmetric Hadamard matrices was originally based on circulant symmetric $\\pm 1$ matrices, called \\textit{propus matrices}. We also give another construction based on symmetric Williamson-type matrices.\n  We give constructions to find symmetric propus-Hadamard matrices for 57 orders $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01732","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"}