{"paper":{"title":"A general construction of Ordered Orthogonal Arrays using LFSRs","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brett Stevens, Daniel Panario, Daniel Wevrick, Mark Saaltink","submitted_at":"2018-05-25T20:06:50Z","abstract_excerpt":"In \\cite{Castoldi}, $q^t \\by (q+1)t$ ordered orthogonal arrays (OOAs) of strength $t$ over the alphabet $\\FF_q$ were constructed using linear feedback shift register sequences (LFSRs) defined by {\\em primitive} polynomials in $\\FF_q[x]$. In this paper we extend this result to all polynomials in $\\FF_q[x]$ which satisfy some fairly simple restrictions, restrictions that are automatically satisfied by primitive polynomials. While these restrictions sometimes reduce the number of columns produced from $(q+1)t$ to a smaller multiple of $t$, in many cases we still obtain the maximum number of colum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10350","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"}