A Survey of Group Weighing Matrices

Abstract

<p>A weighing matrix is a square (nxn) matrix whose entries are in the set {1,0,-1} and also satisfies the property that the matrix times its transpose is a positive integer multiple times the identity matrix. That is to say: W Wt = k I. The value of k is called the weight of the matrix Wand its size n is the order. A group weighing matrix is a weighing matrix which is acted upon by some group. This refers to the placement of the entries wi,j throughout the matrix. By setting the elements in the first row the group (acting on the matrix) will fill the remaining entries by the formula wi,j = gi gj-1. In this talk we are speaking only of abelian groups. The interest of these structures is whether or not they exist for a given order and weight. We will present properties and known results for the existence of group weighing matrices with orders and weights less than 100.</p><p>This presentation occurred at the Wright State University Campus-Wide Celebration of Research, Scholarship and Creative Activities on April 16, 2010</p>