Construction of generalized Hadamard matrices D( rm( r+1), rm( r+1); p)

Abstract

In this paper, a recurrent method for constructing the generalized Hadamard matrices D( r m ( r+1), r m ( r+1); p), m⩾1, has been given under the condition that both D( r, r; r) and D( r+1, r+1; p) are known. The particular structures of the Hadamard matrices D( r m ( r+1), r m ( r+1); p) (or, equivalently, the orthogonal arrays L r m ( r+1) p (( r m ( r+1)) 1 p r m ( r+1) )) constructed in this paper are also interesting since the matrix images of subarrays of the corresponding orthogonal arrays have clear and simple forms which can be obtained easily. The property can be used to construct the other new difference matrices and orthogonal arrays by using the methods of orthogonal decompositions of projection matrices (Zhang, Lu, Pang, Statist. Sinica 9 (1999) 595).