Abstract
Abstract An m-flat association scheme, denoted 𝔛(Xn (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 Jq (n, m). In this paper, the character table of 𝔛(Xn (m)) is obtained from that of Jq (n, m) by studying the relationship between the parameter sets of two association schemes.
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