{"paper":{"title":"Linearized polynomials over finite fields revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Baofeng Wu, Zhuojun Liu","submitted_at":"2012-11-23T11:36:32Z","abstract_excerpt":"We give new characterizations of the algebra $\\mathscr{L}_n(\\mathbb{F}_{q^n})$ formed by all linearized polynomials over the finite field $\\mathbb{F}_{q^n}$ after briefly surveying some known ones. One isomorphism we construct is between $\\mathscr{L}_n(\\mathbb{F}_{q^n})$ and the composition algebra $\\mathbb{F}_{q^n}^\\vee\\otimes_{\\mathbb{F}_{q}}\\mathbb{F}_{q^n}$. The other isomorphism we construct is between $\\mathscr{L}_n(\\mathbb{F}_{q^n})$ and the so-called Dickson matrix algebra $\\mathscr{D}_n(\\mathbb{F}_{q^n})$. We also further study the relations between a linearized polynomial and its ass"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5475","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"}