On codes meeting the Griesmer bound.
type: Item
instance of: scholarly article
title: On codes meeting the Griesmer bound.
zbMATH Open document ID: 1045.94022
DOI: 10.1016/S0012-365X(03)00201-2
published in: Discrete Mathematics
publication date: 2004-01-26T00:00:00Z
review text: The main results in this paper are the following two theorems: Theorem 9. Let \(s+t<q\) and \(k\geq4\). Each \([g_q(k,d),k,d]_q\) code with \[ sq^{k-1}-(s+t)q^{k-2}-q^{k-4}\leq d<sq^{k-1}-(s+t)q^{k-2} \] can be extended to a \([g_q(k,d'),k,d']_q\) code with \(d'=sq^{k-1}-(s+t)q^{k-2}\). Theorem 12. If \((s+t)^2+3(s+t)+1\leq q\), then each \([g_q(k,d),k,d]_q\) code with \[ sq^{k-1}-(s+t)q^{k-2}-q^{k-3}+1\leq d< sq^{k-1}-(s+t)q^{k-2} \] and \(k\geq3\) can be extended to a \([g_q(k,d'),k,d']_q\) code with \(d'=sq^{k-1}-(s+t)q^{k-2}\).
Mathematics Subject Classification ID: 94B65
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 2032868
zbMATH Keywords: linear codes
zbMATH Keywords: Griesmer codes
zbMATH Keywords: code extensions
zbMATH Keywords: Griesmer bound
author: Andreas Klein
reviewed by: I. Landjev
MaRDI profile type: Publication
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full work available at URL: s0012-365x(03)00201-2
OpenAlex ID: W2089318832
description: scientific article; zbMATH DE number 2032868