{"paper":{"title":"A class of repeated-root constacyclic codes over $\\mathbb{F}_{p^m}[u]/\\langle u^e\\rangle$ of Type $2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Fang-Wei Fu, Hai Q. Dinh, Jian Gao, Songsak Sriboonchitta, Yonglin Cao, Yuan Cao","submitted_at":"2018-05-15T07:06:02Z","abstract_excerpt":"Let $\\mathbb{F}_{p^m}$ be a finite field of cardinality $p^m$ where $p$ is an odd prime, $n$ be a positive integer satisfying ${\\rm gcd}(n,p)=1$, and denote $R=\\mathbb{F}_{p^m}[u]/\\langle u^e\\rangle$ where $e\\geq 4$ be an even integer. Let $\\delta,\\alpha\\in \\mathbb{F}_{p^m}^{\\times}$. Then the class of $(\\delta+\\alpha u^2)$-constacyclic codes over $R$ is a significant subclass of constacyclic codes over $R$ of Type 2. For any integer $k\\geq 1$, an explicit representation and a complete description for all distinct $(\\delta+\\alpha u^2)$-constacyclic codes over $R$ of length $np^k$ and their dua"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05595","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"}