{"paper":{"title":"A class of constacyclic codes over $\\mathbb{F}_{p^m}[u]/\\left<u^2\\right>$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.IT"],"primary_cat":"cs.IT","authors_text":"Anuradha Sharma, Saroj Rani","submitted_at":"2017-07-12T03:52:07Z","abstract_excerpt":"Let $p$ be an odd prime, and let $m$ be a positive integer satisfying $p^m \\equiv 3~(\\text{mod }4).$ Let $\\mathbb{F}_{p^m}$ be the finite field with $p^m$ elements, and let $R=\\mathbb{F}_{p^m}[u]/\\left<u^2\\right>$ be the finite commutative chain ring with unity. In this paper, we determine all constacyclic codes of length $4p^s$ over $R$ and their dual codes, where $s$ is a positive integer. We also determine their sizes and list some isodual constacyclic codes of length $4p^s$ over $R.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06133","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"}