Constructions for orthogonal designs using signed group orthogonal designs

TL;DR

This paper explores the use of signed group orthogonal designs to construct various orthogonal designs, demonstrating their effectiveness in generating different types of orthogonal matrices and expanding the theoretical framework.

Contribution

It introduces new constructions of orthogonal designs using signed group orthogonal designs, highlighting their potential in producing diverse orthogonal matrices.

Findings

Constructed new families of orthogonal designs

Demonstrated the versatility of signed group orthogonal designs

Extended the theoretical understanding of orthogonal design generation

Abstract

Craigen introduced and studied signed group Hadamard matrices extensively and eventually provided an asymptotic existence result for Hadamard matrices. Following his lead, Ghaderpour introduced signed group orthogonal designs and showed an asymptotic existence result for orthogonal designs and consequently Hadamard matrices. In this paper, we construct some interesting families of orthogonal designs using signed group orthogonal designs to show the capability of signed group orthogonal designs in generation of different types of orthogonal designs.