Weighing matrices: generalizations and related configurations

Abstract

It is the purpose of this thesis to explore the relationships that exist between weighing matrices, including their generalizations, and various other combinatorial configurations.

Principally, it will be shown that any balanced generalized weighing matrix with entries from a finite abelian group is equivalent to the existence of families of commutative association schemes.

Additionally, novel constructions of related combinatorial configurations are presented such as balancedly splittable orthogonal designs and new families of balanced weighing matrices.