{"paper":{"title":"Dual of Codes over Finite Quotients of Polynomial Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.RA"],"primary_cat":"cs.IT","authors_text":"Ashkan Nikseresht","submitted_at":"2016-05-11T09:55:01Z","abstract_excerpt":"Let $A=\\frac{\\mathbb{F}[x]}{\\langle f(x)\\rangle }$, where $f(x)$ is a monic polynomial over a finite field $\\mathbb{F}$. In this paper, we study the relation between $A$-codes and their duals. In particular, we state a counterexample and a correction to a theorem of Berger and El Amrani (Codes over finite quotients of polynomial rings, \\emph{Finite Fields Appl.} \\textbf{25} (2014), 165--181) and present an efficient algorithm to find a system of generators for the dual of a given $A$-code. Also we characterize self-dual $A$-codes of length 2 and investigate when the $\\mathbb{F}$-dual of $A$-co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03356","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"}