Abstract
Let f be a monic, irreducible polynomial of degree n in F q [ x ] and let CM ( f , q ) be the set of all roots of the polynomial f in the algebra M ( n , q ) of all n × n matrices over F q . The action of the general linear group GL ( n , q ) on CM ( f , q ) × CM ( f , q ) by inner automorphisms defines an association scheme. For given q all association schemes CM ( f , q ) determined by irreducible polynomials of degree n are isomorphic. When deg f = 2 , then the association scheme CM ( f , q ) is symmetric and in this case we determine the intersection numbers.
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