New bounds for \(n_{4}(k,d)\) and classification of some optimal codes over GF(4)
type: Item
instance of: scholarly article
title: New bounds for \(n_{4}(k,d)\) and classification of some optimal codes over GF(4)
zbMATH Open document ID: 1054.94021
author: M. Grassl
author: Iliya G. Bouyukliev
author: Zlatko Varbanov
published in: Discrete Mathematics
publication date: 2004-08-06T00:00:00Z
review text: The authors study the problem of determining the value of \(n_4(k,d)\) -- the shortest possible length of a quaternary code of fixed dimension \(k\) and fixed minimum distance \(d\). For values of \(k\) smaller than 5, this problem has been solved for all \(d\). For 5-dimensional codes there were some 200 undecided values for \(d\). The authors provide lots of constructions thus finding many exact values or improving bounds on \(n_4(5,d)\). They leave 132 undecided values of \(d\) for which \(n_4(5,d)\) is still unknown. The paper contains also an enumeration for some short optimal quaternary codes of dimension \(k=3,4,5,6\).
Mathematics Subject Classification ID: 94B65
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 51E22
zbMATH DE Number: 2083658
zbMATH Keywords: quaternary linear codes
zbMATH Keywords: optimal codes
zbMATH Keywords: Griesmer bound
reviewed by: I. Landjev
describes a project that uses: Magma
describes a project that uses: Code Tables
MaRDI profile type: Publication
full work available at URL: j.disc.2003.11.003
OpenAlex ID: W2067373633
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DOI: 10.1016/J.DISC.2003.11.003
description: scientific article; zbMATH DE number 2083658