{"paper":{"title":"Explicit representation for a class of Type 2 constacyclic codes over the ring $\\mathbb{F}_{2^m}[u]/\\langle u^{2\\lambda}\\rangle$ with even length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Guidong Wang, Hai Q. Dinh, Songsak Sriboonchitta, Yonglin Cao, Yuan Cao","submitted_at":"2019-05-08T13:00:02Z","abstract_excerpt":"Let $\\mathbb{F}_{2^m}$ be a finite field of cardinality $2^m$, $\\lambda$ and $k$ be integers satisfying $\\lambda,k\\geq 2$ and denote $R=\\mathbb{F}_{2^m}[u]/\\langle u^{2\\lambda}\\rangle$. Let $\\delta,\\alpha\\in \\mathbb{F}_{2^m}^{\\times}$. For any odd positive integer $n$, we give an explicit representation and enumeration for all distinct $(\\delta+\\alpha u^2)$-constacyclic codes over $R$ of length $2^kn$, and provide a clear formula to count the number of all these codes. As a corollary, we conclude that every $(\\delta+\\alpha u^2)$-constacyclic code over $R$ of length $2^kn$ is an ideal generated"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03621","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"}