Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Mathematics and Statistics

First Advisor

Dursun Bulutoglu, PhD


Well-designed experiments greatly improve test and evaluation. Efficient experiments reduce the cost and time of running tests while improving the quality of the information obtained. Orthogonal Arrays (OAs) and Hadamard matrices are used as designed experiments to glean as much information as possible about a process with limited resources. However, constructing OAs and Hadamard matrices in general is a very difficult problem. Finding Legendre pairs (LPs) results in the construction of Hadamard matrices. This research studies the classification problem of OAs and the existence problem of LPs. In doing so, it makes two contributions to the discipline. First, it improves upon previous classification results of 2-symbol OAs of even-strength t and t+2 columns. Second, it presents previously unknown impossible values for the dimension of the convex hull of all feasible points to the LP problem improving our understanding of its feasible set.

AFIT Designator


DTIC Accession Number