{"paper":{"title":"Matrix-product structure of constacyclic codes over finite chain rings $\\mathbb{F}_{p^m}[u]/\\langle u^e\\rangle$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Fang-Wei Fu, Yonglin Cao, Yuan Cao","submitted_at":"2018-03-03T02:50:16Z","abstract_excerpt":"Let $m,e$ be positive integers, $p$ a prime number, $\\mathbb{F}_{p^m}$ be a finite field of $p^m$ elements and $R=\\mathbb{F}_{p^m}[u]/\\langle u^e\\rangle$ which is a finite chain ring. For any $\\omega\\in R^\\times$ and positive integers $k, n$ satisfying ${\\rm gcd}(p,n)=1$, we prove that any $(1+\\omega u)$-constacyclic code of length $p^kn$ over $R$ is monomially equivalent to a matrix-product code of a nested sequence of $p^k$ cyclic codes with length $n$ over $R$ and a $p^k\\times p^k$ matrix $A_{p^k}$ over $\\mathbb{F}_p$. Using the matrix-product structures, we give an iterative construction o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01095","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"}