On non-symmetric commutative association schemes with exactly one pair
of non-symmetric relations

G.L. CHIA and W.K. KOK

Research Report No. 4/2002

Abstract

For a given non-symmetric commutative association scheme, by fusing all the non-symmetric relations pairwise with their symmetric counterparts, we can obtain a new symmetric association scheme. In this paper, we introduce a set of feasibility and realizability conditions for a class e symmetric association scheme to be split into a class e+1 non-symmetric association scheme. By applying the realizability conditions, the construction of certain non-symmetric commutative association schemes can be reduced to the construction of certain Hadamard matrices.