Some orthogonal designs and complex Hadamard matrices by using two Hadamard matrices

Authors

Jennifer Seberry, University of WollongongFollow
Xian-Mo Zhang, University of WollongongFollow

Publication Details

Jennifer Seberry and Xian-Mo Zhang, Some orthogonal designs and complex Hadamard matrices by using two Hadamard matrices, Australasian Journal of Combinatorics, 4, (1991), 93-102.

Abstract

We prove that if there exist Hadamard matrices of order h and n divisible by 4 then there exist two disjoint W(¹/₄hn, ¹/₈hn), whose sum is a (1, -1) matrix and a complex Hadamard matrix of order ¹/₄hn, furthermore, if there exists an OD(m; s₁, s₂,··· ,s_l) for even m then there exists an OD(¹/₄hnm; ¹/₄hns₁, ¹/₄hns₂,···, ¹/₄hns_l).