Association algebras for finite projective planes

Abstract

The plane 71 is a finite plane when the set of points is finite and it is an elementary consequence of the above axioms that finite planes have n* + n + 1 lines and the same number of points. Such a plane is said to be of order n [4]. In this paper, we study projective planes of order n and show how to associate a commutative algebra of matrices with each plane. This algebra is the Bose-Mesner algebra which exists whenever there exists an association scheme on some set X. In Section 2 we are able to give necessary and suflicient conditions for the existence of a plane of order n.