{"paper":{"title":"Construction of the mutually orthogonal extraordinary supersquares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Cristian Ghiu, Iulia Ghiu","submitted_at":"2013-04-30T17:35:10Z","abstract_excerpt":"Our purpose is to determine the complete set of mutually orthogonal squares of order $d$, which are not necessary Latin. In this article, we introduce the concept of supersquare of order $d$, which is defined with the help of its generating subgroup in $\\mathbb{F}_d\\times \\mathbb{F}_d$. We present a method of construction of the mutually orthogonal supersquares. Further, we investigate the orthogonality of extraordinary supersquares, a special family of squares, whose generating subgroups are extraordinary. The extraordinary subgroups in $\\mathbb{F}_d\\times \\mathbb{F}_d$ are of great importanc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.8086","kind":"arxiv","version":3},"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"}