Lower bounds for \(q\)-ary codes of covering radius one
type: Item
instance of: scholarly article
title: Lower bounds for \(q\)-ary codes of covering radius one
zbMATH Open document ID: 0947.94031
DOI: 10.1016/S0012-365X(99)00338-6
author: Wolfgang Haas
published in: Discrete Mathematics
publication date: 2000-08-03T00:00:00Z
review text: Let \(k_q(n)\) denote the minimal cardinality of a \(q\)-ary code \(C\) of length \(n\) and covering radius one. In this paper the author derives lower bounds for \(k_q(n)\). As an application it is shown that the difference between \(k_q(n)\) and the sphere covering bound approaches infinity with increasing \(n\) if \(q\) is fixed and \((q-1)n+1\) does not divide \(q^n\). The author improves a few already known lower bounds listed in [\textit{G. Cohen}, \textit{I. Honkala}, \textit{S. Litsyn} and \textit{A. Lobstein}, Covering codes. North-Holland Mathematical Library. 54, Amsterdam: Elsevier (1997; Zbl 0874.94001)]. For instance, it is shown that \(k_2(21)\geq 95360\) and \(k_3(10)\geq 2835\).
Mathematics Subject Classification ID: 94B75
Mathematics Subject Classification ID: 94B65
zbMATH DE Number: 1462320
zbMATH Keywords: minimal cardinality
zbMATH Keywords: \(q\)-ary code
zbMATH Keywords: covering radius one
zbMATH Keywords: lower bounds
zbMATH Keywords: sphere covering bound
MaRDI profile type: Publication
full work available at URL: s0012-365x(99)00338-6
OpenAlex ID: W1969442043
description: scientific article; zbMATH DE number 1462320