Balancedly splittable orthogonal designs and equiangular tight frames

TL;DR

This paper introduces balancedly splittable orthogonal designs and provides a recursive construction, leading to the creation of equiangular tight frames that meet the Delsarte-Goethals-Seidel bound across real, complex, and quaternionic cases.

Contribution

It introduces the concept of balancedly splittable orthogonal designs and offers a recursive construction method, advancing the design of optimal equiangular tight frames.

Findings

Construction of equiangular tight frames meeting the Delsarte-Goethals-Seidel bound

Introduction of balancedly splittable orthogonal designs

Recursive method for design construction

Abstract

The concept of balancedly splittable orthogonal designs is introduced along with a recursive construction. As an application, equiangular tight frames over the real, complex, and quaternions meeting the Delsarte-Goethals-Seidel upper bound is obtained.