Publication Date


Document Type


Committee Members

K. T. Arasu (Advisor), Yuqing Chen (Committee Member), Xiaoyu Liu (Committee Member)

Degree Name

Master of Science (MS)


A weighing matrix is a square matrix whose entries are 1, 0 or -1 and has the property that the matrix times its transpose is some integer multiple of the identity matrix. We examine the case where these matrices are said to be developed by an abelian group. Through a combination of extending previous results and by giving explicit constructions we will answer the question of existence for 318 such matrices of order and weight both below 100. At the end, we are left with 98 open cases out of a possible 1,022. Further, some of the new results provide insight into the existence of matrices with larger weights and orders.

Page Count


Department or Program

Department of Mathematics and Statistics

Year Degree Awarded