  The notion of multivariate $P$- and $Q$-polynomial association scheme has
been introduced recently, generalizing the well-known univariate case. Numerous
examples of such association schemes have already been exhibited. In
particular, it has been demonstrated that the non-binary Johnson scheme is a
bivariate $P$-polynomial association scheme. We show here that it is also a
bivariate $Q$-polynomial association scheme for some parameters. This provides,
with the $P$-polynomial structure, the bispectral property (i.e. the recurrence
and difference relations) of a family of bivariate orthogonal polynomials made
out of univariate Krawtchouk and dual Hahn polynomials. The algebra based on
the bispectral operators is also studied together with the subconstituent
algebra of this association scheme.
