GEOMETRIC CONSTRUCTION OF ASSOCIATION SCHEMES FROM DEGENERATE QUADRICS IN PROJECTIVE SPACES PG(2V+δ+ι-1, F_q)FOR q ODD

摘要

Let F_q be a finite field with q elements, where q is a power of an odd prime. In this paper, the authors consider a projective space PG(2V+δ+ι-1, F_q) with dimension 2V+δ+ι, partitioned into an affine space AG(2V+δ+ι-1, F_q) of dimension 2V+δ+ι and a hyperplane H= PG(2V+δ+ι-1, F_q) of dimension 2V+δ+ι-1 at infinity, where ι≠0. The points of the hyperplane H are next partitioned into four subsets. A pair of points α And b of the affine space is defined to belong to class I if the line ab meets the subset I of H. Finally, a family of four-class association schemes are constructed, and parameters are Also computed.