{"paper":{"title":"One-Lee weight and two-Lee weight $\\mathbb{Z}_2\\mathbb{Z}_2[u]$-additive codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.RA","authors_text":"Liqi Wang, Shixin Zhu, Xiaoshan Kai, Zhenliang Lu","submitted_at":"2016-09-30T04:45:00Z","abstract_excerpt":"In this paper, we study one-Lee weight and two-Lee weight codes over $\\mathbb{Z}_{2}\\mathbb{Z}_{2}[u]$, where $u^{2}=0$. Some properties of one-Lee weight $\\mathbb{Z}_{2}\\mathbb{Z}_{2}[u]$-additive codes are given, and a complete classification of one-Lee weight $\\mathbb{Z}_2\\mathbb{Z}_2[u]$-additive formally self-dual codes is obtained. The structure of two-Lee weight projective $\\mathbb{Z}_2\\mathbb{Z}_2[u]$ codes is determined. Some optimal binary linear codes are obtained directly from one-Lee weight and two-Lee weight $\\mathbb{Z}_{2}\\mathbb{Z}_{2}[u]$-additive codes via the extended Gray m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09588","kind":"arxiv","version":3},"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"}