{"paper":{"title":"On Euclidean and Hermitian Self-Dual Cyclic Codes over $\\mathbb{F}_{2^r}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.NT"],"primary_cat":"cs.IT","authors_text":"Lilibeth D. Valdez, Odessa D. Consorte","submitted_at":"2016-03-11T05:04:14Z","abstract_excerpt":"Cyclic and self-dual codes are important classes of codes in coding theory. Jia, Ling and Xing \\cite{Jia} as well as Kai and Zhu \\cite{Kai} proved that Euclidean self-dual cyclic codes of length $n$ over $\\mathbb{F}_q$ exist if and only if $n$ is even and $q=2^r$, where $r$ is any positive integer. For $n$ and $q$ even, there always exists an $[n, \\frac{n}{2}]$ self-dual cyclic code with generator polynomial $x^{\\frac{n}{2}}+1$ called the \\textit{trivial self-dual cyclic code}. In this paper we prove the existence of nontrivial self-dual cyclic codes of length $n=2^\\nu \\cdot \\bar{n}$, where $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03520","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"}