On a new class of productive regular Hadamard matrices
type: Item
instance of: scholarly article
title: On a new class of productive regular Hadamard matrices
zbMATH Open document ID: 1106.05018
author: Majid Behbahani
author: H. Kharaghani
published in: Discrete Mathematics
publication date: 2006-12-14T00:00:00Z
review text: By definition a Hadamard matrix is a \(\pm 1\)-square matrix with orthogonal rows. If the sum of rows of a Hadamard matrix \(H\) is constant then \(H\) is called regular, and it is necessarily of order \(4n^{2}\) with constant row sum \(2n\). In [\textit{Y. J. Ionin}, Des. Codes Cryptography 32, 227--233 (2004; Zbl 1047.05002)] the concept of a productive Hadamard matrix is defined and it is proved that the existence of certain productive matrices implies the existence of certain symmetric designs. In the paper under review the authors prove that if there is a Hadamard matrix of order \(4n\) and \(m=8n^{2}-1\equiv 3\pmod 4\) is a prime power, then there is a regular Hadamard matrix of order \(16n^{2}(8n^{2}-1)^{2}\). Then they proceed to show that many of the regular Hadamard matrices constructed with the above conditions are productive. Hence they apply the result of Ionin's paper quoted above to produce infinite new classes of symmetric designs.
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 5080047
zbMATH Keywords: Bush-type Hadamard matrices
zbMATH Keywords: Mathon matrices
zbMATH Keywords: balanced generalized weighing matrices
zbMATH Keywords: symmetric designs
reviewed by: M. R. Darafsheh
MaRDI profile type: Publication
full work available at URL: j.disc.2005.02.023
OpenAlex ID: W2005448597
cites work: New symmetric designs from regular Hadamard matrices
cites work: Regular Hadamard matrices generating infinite families of symmetric designs
cites work: On Automorphism Groups of Divisible Designs
cites work: Perfect codes and balanced generalized weighing matrices
cites work: Q3708813
cites work: Symmetric Conference Matrices of Order pq 2 + 1
cites work: New Hadamard matrices and conference matrices obtained via Mathon's construction
DOI: 10.1016/J.DISC.2005.02.023
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description: scientific article; zbMATH DE number 5080047