Unbiased and skew-regular Hadamard matrices

Abstract

This thesis explores the concept of regularity in Hadamard matrices. By generalizing the definition of regularity, researchers have combined the definitions of skew-type and regular Hadamard matrices to define skew-regular-Hadamard matrices. In this thesis, we consider skew-regularity in the context of both real and quaternary Hadamard matrices, and showcase some known applications of these objects. The concept of regularity appears in the definition of unbiasedness. Aided by our knowledge of regularity, we then explore unbiasedness for both real and quaternary Hadamard matrices, and classify small orders of mutually unbiased quaternary Hadamard matrices.