{"paper":{"title":"A characterization of $\\mathbb{Z}_2\\mathbb{Z}_2[u]$-linear codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Joaquim Borges","submitted_at":"2016-11-17T12:27:33Z","abstract_excerpt":"We prove that the class of $\\Z_2\\Z_2[u]$-linear codes is exactly the class of $\\Z_2$-linear codes with automorphism group of even order. Using this characterization, we give examples of known codes, e.g. perfect codes, which has a nontrivial $\\Z_2\\Z_2[u]$ structure. We also exhibit an example of a $\\Z_2$-linear code which is not $\\Z_2\\Z_2[u]$-linear. Also, we state that duality of $\\Z_2\\Z_2[u]$-linear codes is the same that duality of $\\Z_2$-linear codes.\n  Finally, we prove that the class of $\\Z_2\\Z_4$-linear codes which are also $\\Z_2$-linear is strictly contained in the class of $\\Z_2\\Z_2[u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05655","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"}