On the achievement of the Griesmer bound
type: Item
instance of: scholarly article
title: On the achievement of the Griesmer bound
zbMATH Open document ID: 0887.94016
DOI: 10.1023/A:1008250010928
author: Tatsuya Maruta
published in: Designs, Codes and Cryptography
publication date: 1998-05-29T00:00:00Z
review text: For \(d=(k-2)q^{k-1} -(k-1)q^{k-2}\), there does not exist a linear \((n,k)\)-code over \(GF(q)\) of minimum Hamming distance \(d\) which attains the Grieser bound for \(q\geq k\), \(k=3,4,5\) and for \(q\geq 2k-3\), \(k\geq 6\). For \(q\geq k\) and \(k=3,4\) this has been known before [\textit{S. M. Dodunekov}, C. R. Acad. Bulg. Sci. 39, 39-41 (1986; Zbl 0628.94014), and T. Maruta (1995)]. The remaining parts of the theorem are proved by considering the columns of a generator matrix of an \((n,k,d)_q\)-code as a multiset of \(n\) points in the projective space \(PG(k-1,q)\).
Mathematics Subject Classification ID: 94B65
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 1051433
zbMATH Keywords: linear code
zbMATH Keywords: Grieser bound
zbMATH Keywords: projective space
reviewed by: Ralph-Hardo Schulz
MaRDI profile type: Publication
full work available at URL: a:1008250010928
OpenAlex ID: W1481844012
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description: scientific article; zbMATH DE number 1051433