Publication Details

This article was originally published as Georgiou, S, Koukouvinos, C and Seberry, J, Generalized orthogonal designs, Ars Combinatoria, 2004, 71, 33-48. The original journal can be found here. Copyright 2004 The Charles Babbage Research Centre.


Orthogonal designs and their special cases such as weighing matrices and Hadamard matrices have many applications in combinatorics, statistics, and coding theory as well as in signal processing. In this paper we generalize the definition of orthogonal designs, we give many constructions for these designs and we prove some multiplication theorems that, most of them, can also be applied in the special case of orthogonal designs. Some necessary conditions for the existence of generalized orthogonal designs are also given.