{"paper":{"title":"Complete classification of $(\\delta+\\alpha u^2)$-constacyclic codes over $\\mathbb{F}_{2^m}[u]/\\langle u^4\\rangle$ of oddly even length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Yonglin Cao, Yuan Cao","submitted_at":"2016-09-20T09:28:04Z","abstract_excerpt":"Let $\\mathbb{F}_{2^m}$ be a finite field of cardinality $2^m$, $R=\\mathbb{F}_{2^m}[u]/\\langle u^4\\rangle)$ and $n$ is an odd positive integer. For any $\\delta,\\alpha\\in \\mathbb{F}_{2^m}^{\\times}$, ideals of the ring $R[x]/\\langle x^{2n}-(\\delta+\\alpha u^2)\\rangle$ are identified as $(\\delta+\\alpha u^2)$-constacyclic codes of length $2n$ over $R$. In this paper, an explicit representation and enumeration for all distinct $(\\delta+\\alpha u^2)$-constacyclic codes of length $2n$ over $R$ are presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06065","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"}