{"paper":{"title":"Dual codes of product semi-linear codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.RA"],"primary_cat":"cs.IT","authors_text":"Andrea Luigi Tironi, Luis Felipe Tapia Cuiti\\~no","submitted_at":"2013-06-05T01:30:05Z","abstract_excerpt":"Let $\\mathbb{F}_q$ be a finite field with $q$ elements and denote by $\\theta : \\mathbb{F}_q\\to\\mathbb{F}_q$ an automorphism of $\\mathbb{F}_q$. In this paper, we deal with linear codes of $\\mathbb{F}_q^n$ invariant under a semi-linear map $T:\\mathbb{F}_q^n\\to\\mathbb{F}_q^n$ for some $n\\geq 2$. In particular, we study three kind of their dual codes, some relations between them and we focus on codes which are products of module skew codes in the non-commutative polynomial ring $\\mathbb{F}_q[X,\\theta]$ as a subcase of linear codes invariant by a semi-linear map $T$. In this setting we give also an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0957","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"}