Character tables of m-flat association schemes

An m-flat association scheme, denoted X(X-n(m)), is defined on the set of affine m-flats, the cosets of an m-dimensional subspace of an n-dimensional vector space over the finite field F-q. This association scheme was introduced by Zhu and Li in "A construction of association schemes with several association classes and of PBIB designs using m-flats in finite affine geometries", Acta Math. Appl. Sinica 20 (1), 155-158, 1997. This association scheme is known to be imprimitive and gives rise to a quotient scheme that is isomorphic to the q-analogue Johnson scheme J(q)(n, m). In this paper, the character table of X(X-n(m)) is obtained from that of J(q)(n, m) by studying the relationship between the parameter sets of two association schemes.