CONSTRUCTION OF AMICABLE MATRICES AND GENERALIZED ORTHOGONAL DESIGNS OVER THE PRIME FIELDS F(p)

Generalized orthogonal designs have many useful applications in statistics, web engineering, and coding theory along with signal processing. In this paper, for every prime number p > 3, we develop a method of constructing a set of four circulant amicable matrices {V-i} satisfying ViViT = q(i)I(n) (I-n is the identity matrix of order n) over the prime field F(p) Using these matrices with T-matrices, we suggest some approaches to construct infinite classes of generalized orthogonal designs (GODs) over the prime fields F(p).