Construction of generalized Hadamard matrices \(D(r^m(r+1),r^m(r+1);p)\)
type: Item
instance of: scholarly article
title: Construction of generalized Hadamard matrices \(D(r^m(r+1),r^m(r+1);p)\)
zbMATH Open document ID: 0996.05020
DOI: 10.1016/S0378-3758(01)00249-X
author: Lian Duan
author: Yiqiang Lu
author: Zhongguo Zheng
author: Yingshan Zhang
published in: Journal of Statistical Planning and Inference
publication date: 2002-08-28T00:00:00Z
review text: A difference matrix \(D(\lambda p,m;p)\) is a \(\lambda p \times m\) matrix, with entries in \(G\), where \(G\) is a finite abelian group of order \(p\), such that the vector difference of any two columns contains each element of \(G\) \(\lambda \) times. A generalized Hadamard matrix is a difference matrix with \(\lambda p =m.\) The authors give a method for constructing generalized Hadamard matrices \(D(r^m(r+1),r^m(r+1);p)\) for \(n \geq 1\) from known \(D(r,r;r)\) and \(D(r+1,r+1;p)\) generalized Hadamard matrices. The orthogonal arrays \(L_{r^m(r+1)_p}((r^m(r+1))^1p^{r^m(r+1)})\) are equivalent to these constructed Hadamard matrices. These structures are then used to construct other difference matrices and orthogonal arrays using orthogonal decomposition of projection matrices.
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 1790178
zbMATH Keywords: difference matrix
zbMATH Keywords: generalized Hadamard matrix
zbMATH Keywords: orthogonal array
zbMATH Keywords: permutation matrix
zbMATH Keywords: projection matrix
zbMATH Keywords: Kronecker sum
reviewed by: Steven T. Dougherty
MaRDI profile type: Publication
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full work available at URL: s0378-3758(01)00249-x
OpenAlex ID: W2029839804
description: scientific article; zbMATH DE number 1790178