SBIBD(4k\({}^ 2,2k^ 2+k,k^ 2+k)\) and Hadamard matrices of order \(4k^ 2\) with maximal excess are equivalent
type: Item
instance of: scholarly article
title: SBIBD(4k\({}^ 2,2k^ 2+k,k^ 2+k)\) and Hadamard matrices of order \(4k^ 2\) with maximal excess are equivalent
zbMATH Open document ID: 0713.05017
DOI: 10.1007/BF01788694
published in: Graphs and Combinatorics
publication date: 1989-01-01T00:00:00Z
review text: The sum of the elements of an Hadamard matrix \({\mathcal H}\) is denoted by o(\({\mathcal H})\) and called excess of \({\mathcal H}\). \(o(n)=\max o({\mathcal H})\) for all Hadamard matrices of order n. It is well-known that o(n)\(\leq n\sqrt{n}\). In this paper the following statement is proved. Theorem. There is an Hadamard matrix of order \(4s^ 2\) and maximal excess \(8s^ 2\) if and only if there is an \(SBIBD(4s^ 2,2s^ 2+s,s^ 2+s).\) It is shown that \(SBIBD(4s^ 2,2s^ 2+s,s^ 2+s)\) is equivalent to existence of a regular Hadamard matrix of order \(4s^ 2\) whith maximal excess.
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 4172992
zbMATH Keywords: regular Hadamard matrix
zbMATH Keywords: maximal excess
author: Jennifer Seberry
reviewed by: S. S. Agayan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4172992