\((2s-1)\)-designs with \(s\) intersection numbers
type: Item
instance of: scholarly article
title: \((2s-1)\)-designs with \(s\) intersection numbers
zbMATH Open document ID: 0795.05022
DOI: 10.1007/BF01264071
author: M. S. Shrikhande
author: Yury J. Ionin
published in: Geometriae Dedicata
publication date: 1994-08-29T00:00:00Z
review text: The authors call a \((2s-1)\)-design with \(s\) intersection numbers extremal. Expressing the coefficients of the Delsarte polynomial for an extremal design in a suitable manner, they obtain several interesting necessary conditions on the parameters and intersection numbers of such designs. They establish that for a fixed \(\lambda\) and \(s \geq 3\), there exist at most finitely many extremal designs. They also show that an extremal design with \(s\) intersection numbers is the Witt 5-(24,8,1) design if and only if \(s \geq 3\) and the sum of the intersection numbers is at most \(s(s-1)\).
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 493323
zbMATH Keywords: Delsarte polynomial
zbMATH Keywords: extremal design
zbMATH Keywords: intersection numbers
reviewed by: Chester J. Salwach
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 493323