{"paper":{"title":"A family of constacyclic codes over $\\mathbb{F}_{2^{m}}+u\\mathbb{F}_{2^{m}}$ and its application to quantum codes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Shixin Zhu, Ting Yao, Xiaoshan Kai, Yongsheng Tang","submitted_at":"2017-12-06T08:31:33Z","abstract_excerpt":"We introduce a Gray map from $\\mathbb{F}_{2^{m}}+u\\mathbb{F}_{2^{m}}$ to $\\mathbb{F}_{2}^{2m}$ and study $(1+u)$-constacyclic codes over $\\mathbb{F}_{2^{m}}+u\\mathbb{F}_{2^{m}},$ where $u^{2}=0.$ It is proved that the image of a $(1+u)$-constacyclic code length $n$ over $\\mathbb{F}_{2^{m}}+u\\mathbb{F}_{2^{m}}$ under the Gray map is a distance-invariant quasi-cyclic code of index $m$ and length $2mn$ over $\\mathbb{F}_{2}.$ We also prove that every code of length $2mn$ which is the Gray image of cyclic codes over $\\mathbb{F}_{2^{m}}+u\\mathbb{F}_{2^{m}}$ of length $n$ is permutation equivalent to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02081","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"}