{"paper":{"title":"On a class of $(\\delta+\\alpha u^2)$-constacyclic codes over $\\mathbb{F}_{q}[u]/\\langle u^4\\rangle$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jian Gao, Yonglin Cao, Yuan Cao","submitted_at":"2015-11-07T16:07:42Z","abstract_excerpt":"Let $\\mathbb{F}_{q}$ be a finite field of cardinality $q$, $R=\\mathbb{F}_{q}[u]/\\langle u^4\\rangle=\\mathbb{F}_{q}+u\\mathbb{F}_{q}+u^2\\mathbb{F}_{q}+u^3\\mathbb{F}_{q}$ $(u^4=0)$ which is a finite chain ring, and $n$ be a positive integer satisfying ${\\rm gcd}(q,n)=1$. For any $\\delta,\\alpha\\in \\mathbb{F}_{q}^{\\times}$, an explicit representation for all distinct $(\\delta+\\alpha u^2)$-constacyclic codes over $R$ of length $n$ is given, and the dual code for each of these codes is determined. For the case of $q=2^m$ and $\\delta=1$, all self-dual $(1+\\alpha u^2)$-constacyclic codes over $R$ of odd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02369","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"}