Mixed difference matrices and the construction of orthogonal arrays
type: Item
instance of: scholarly article
title: Mixed difference matrices and the construction of orthogonal arrays
zbMATH Open document ID: 0901.05020
DOI: 10.1016/0167-7152(95)00105-0
author: Yanyan Li
published in: Statistics \& Probability Letters
publication date: 1998-11-17T00:00:00Z
review text: The authors consider \(n \times k\) matrices with elements from an additive abelian group \(G\), of order \(p\), which they call a \(p\)-level difference matrix, \(D(n,k;p)\), if all the elements of \(G\) appear equally often among the entrywise difference in \(G\). The example of a \(D(6,6;3)\) is also known as a generalized Hadamard matrix, \(\text{GH} (6,6;\text{EA} (2))\). The author gives a construction using the generalized Kronecker product, which gives new orthogonal arrays which are distinct from those of \textit{J. C. Wang} and \textit{C. F. J. Wu} [An approach to the construction of asymmetrical orthogonal arrays, J. Am. Math. Statist. Assoc. 86, No. 414, 450-456 (1991)]. Researchers interested in this topic should also consult \textit{W. de Launey} [GBRDs: Some new constructions for difference matrices, generalized Hadamard matrices and balanced generalized weighing matrices, Graphs Comb. 5, No. 2, 125-135 (1989; Zbl 0687.05011)] and \textit{D. R. Stinson} [Universal hashing and authentication codes, Des. Codes Cryptography 4, No. 4, 369-380 (1994; Zbl 0812.94011)].
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 896119
zbMATH Keywords: mixed difference matrices
zbMATH Keywords: orthogonal arrays
zbMATH Keywords: generalized Kronecker sum
reviewed by: Jennifer Seberry
MaRDI profile type: Publication
full work available at URL: 0167-7152(95)00105-0
OpenAlex ID: W1981571485
cites work: Orthogonal Arrays of Strength two and three
cites work: Q3252271
cites work: Hadamard matrices and their applications
cites work: Q5787292
cites work: Q5181383
Wikidata QID: Q127442652
description: scientific article; zbMATH DE number 896119