{"paper":{"title":"On the existence of primitive completely normal bases of finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giorgos Kapetanakis, Theodoulos Garefalakis","submitted_at":"2017-09-10T17:15:51Z","abstract_excerpt":"Let $\\mathbb{F}_q$ be the finite field of characteristic $p$ with $q$ elements and $\\mathbb{F}_{q^n}$ its extension of degree $n$. We prove that there exists a primitive element of $\\mathbb{F}_{q^n}$ that produces a completely normal basis of $\\mathbb{F}_{q^n}$ over $\\mathbb{F}_q$, provided that $n=p^{\\ell}m$ with $(m,p)=1$ and $q>m$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03141","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"}