{"paper":{"title":"Repeated-root constacyclic codes over the finite chain ring $\\mathbf{ \\mathbb{F}_{p^m}[u]/\\langle u^3 \\rangle }$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anuradha Sharma, Tania Sidana","submitted_at":"2017-06-20T05:01:51Z","abstract_excerpt":"Let $\\mathcal{R}=\\mathbb{F}_{p^m}[u]/\\langle u^3 \\rangle $ be the finite commutative chain ring with unity, where $p$ is a prime, $m$ is a positive integer and $\\mathbb{F}_{p^m}$ is the finite field with $p^m$ elements. In this paper, we determine all repeated-root constacyclic codes of arbitrary lengths over $\\mathcal{R},$ their sizes and their dual codes. As an application, we list some isodual constacyclic codes over $\\mathcal{R}.$ We also determine Hamming distances, RT distances, and RT weight distributions of some repeated-root constacyclic codes over $\\mathcal{R}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08869","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"}