Equivalence of Delsarte's bounds for codes and designs in symmetric association schemes, and some applications
type: Item
instance of: scholarly article
title: Equivalence of Delsarte's bounds for codes and designs in symmetric association schemes, and some applications
zbMATH Open document ID: 0929.05097
DOI: 10.1016/S0012-365X(99)90109-7
author: Vladimir Levenshtein
published in: Discrete Mathematics
publication date: 2000-01-25T00:00:00Z
review text: Delsarte introduced two extremum problems for the systems of \(p\)-numbers and \(q\)-numbers to obtain bounds on the sizes of codes and designs in association schemes. The purpose of this paper is to prove that the Delsarte bound for codes obtained with the help of either of these systems is equivalent to that for designs obtained by using the other system. This means, in particular, that the universal Delsarte bound of 1973 for designs is equivalent to the sphere packing bound for codes. A relationship between bounds for orthogonal arrays and block designs has also been obtained which gives new lower bounds on the size of orthogonal arrays with the help of those for block designs.
reviewed by: Bai Kishan Dass
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05E35
Mathematics Subject Classification ID: 94B65
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 1322035
zbMATH Keywords: codes
zbMATH Keywords: association schemes
zbMATH Keywords: Delsarte bound
zbMATH Keywords: orthogonal arrays
zbMATH Keywords: block designs
MaRDI profile type: Publication
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full work available at URL: s0012-365x(99)90109-7
OpenAlex ID: W3121614802
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description: scientific article; zbMATH DE number 1322035