Abstract

Let F be a finite field with q elements where $q=p\sp{m}, p$ prime. Let ${\cal M}$ be the algebra of n x n circulant matrices over F. The set $O\sb{(n,q)}$ of orthogonal n x n circulant matrices is a subgroup of ${\cal M}\sp\times.$ The major purposes of the thesis are: (1) to explain K. A. Byrd and T. P. Vaughan's results stated in (8), about formulas for the orders, and algorithms for the construction, of the groups $O\sb{(n,q)};$ (2) to show new examples and develop programs to find the orders and to actually construct the group $O\sb{(n,q)}$ for any given n and q.