Generalized Orthogonal Designs

Abstract

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, give many constructions for these designs, and 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.