{"paper":{"title":"All $\\alpha+u\\beta$-constacyclic codes of length $np^{s}$ over $\\mathbb{F}_{p^{m}}+u\\mathbb{F}_{p^{m}}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Wei Zhao, Xilin Tang, Ze Gu","submitted_at":"2016-06-21T05:20:55Z","abstract_excerpt":"Let $\\mathbb{F}_{p^{m}}$ be a finite field with cardinality $p^{m}$ and $R=\\mathbb{F}_{p^{m}}+u\\mathbb{F}_{p^{m}}$ with $u^{2}=0$. We aim to determine all $\\alpha+u\\beta$-constacyclic codes of length $np^{s}$ over $R$, where $\\alpha,\\beta\\in\\mathbb{F}_{p^{m}}^{*}$, $n, s\\in\\mathbb{N}_{+}$ and $\\gcd(n,p)=1$. Let $\\alpha_{0}\\in\\mathbb{F}_{p^{m}}^{*}$ and $\\alpha_{0}^{p^{s}}=\\alpha$. The residue ring $R[x]/\\langle x^{np^{s}}-\\alpha-u\\beta\\rangle$ is a chain ring with the maximal ideal $\\langle x^{n}-\\alpha_{0}\\rangle$ in the case that $x^{n}-\\alpha_{0}$ is irreducible in $\\mathbb{F}_{p^{m}}[x]$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06428","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"}