An elementary derivation of the annihilator polynomial for extremal \((2s+1)\)-designs
type: Item
instance of: scholarly article
title: An elementary derivation of the annihilator polynomial for extremal \((2s+1)\)-designs
zbMATH Open document ID: 0699.05008
DOI: 10.1016/0012-365X(90)90298-V
author: M. S. Shrikhande
author: N. M. Singhi
published in: Discrete Mathematics
publication date: 1990-01-01T00:00:00Z
review text: A \((2s+1)\)-design is known to have at least \(s+1\) block intersection numbers; such a design is extremal when it has exactly \(s+1\). This paper gives an elementary proof of a theorem of Delsarte: the \(s+1\) block intersection numbers of an extremal \((2s+1)\)-design are roots of a polynomial whose coefficients depend only on the design parameters (t- (v,k,\(\lambda)\)). The proof is remarkably concise, and uses a portion of a standard method for decoding BCH codes.
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 4145907
zbMATH Keywords: tight t-design
zbMATH Keywords: annihilator polynomial
Wikidata QID: Q105999529
MaRDI profile type: Publication
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full work available at URL: 0012-365x(90)90298-v
OpenAlex ID: W1970884738
description: scientific article; zbMATH DE number 4145907