Computational Methods in Design Theory

An association scheme A with vertex set X and d classes is a set of symmetric {0, 1}-matrices A0, . . . , Ad with rows and columns indexed by X, such that

1. A0 = I, 2.

∑d i=0 Ai = J ,

3. AiAj lies in the real span of A0, . . . , Ad: AiAj = ∑

Here J denotes the matrix with each entry equal to one (and order determined by context).