{"paper":{"title":"The Gray image of constacyclic codes over the finite chain ring $F_{p^m}[u]/\\langle u^k\\rangle$","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":"2016-10-05T15:07:04Z","abstract_excerpt":"Let $\\mathbb{F}_{p^m}$ be a finite field of cardinality $p^m$, where $p$ is a prime, and $k, N$ be any positive integers. We denote $R_k=F_{p^m}[u]/\\langle u^k\\rangle =F_{p^m}+uF_{p^m}+\\ldots+u^{k-1}F_{p^m}$ ($u^k=0$) and $\\lambda=a_0+a_1u+\\ldots+a_{k-1}u^{k-1}$ where $a_0, a_1,\\ldots, a_{k-1}\\in F_{p^m}$ satisfying $a_0\\neq 0$ and $a_1=1$. Let $r$ be a positive integer satisfying $p^{r-1}+1\\leq k\\leq p^r$. We defined a Gray map from $R_k$ to $F_{p^m}^{p^r}$ first, then prove that the Gray image of any linear $\\lambda$-constacyclic code over $R_k$ of length $N$ is a distance invariant linear $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01471","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"}