Mixed difference matrices and the construction of orthogonal arrays
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)].
scientific article; zbMATH DE number 896119