Computations on Character Tables of Association Schemes

Association schemes are combinatorial objects that allow us solving problems in several branches of mathematics. They have been used in the study of permutation groups and graphs and also in the design of experiments. The author get in touch with this topic through Delsarte’s thesis on association schemes and coding theory [6]. All the information of an association scheme can be derived from its table of characters. In this paper we show some techniques for computing the character table and also derive other properties from it, such as the condition for the scheme to be P-polynomial etc. We also work out some characteristics of metrics which are constant over the relations of the scheme such as Lloyd polynomials. The computations are based on the relation between an association scheme and its Bose-Mesner algebra.