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.

最近引入了多元P和Q多项式关联方案的概念，概括了众所周知的单变量情况。此类关联计划的许多例子已经被展示。特别地，已经证明非二元约翰逊方案是二元P多项式关联方案。我们在这里证明它也是一些参数的双变量Q多项式关联方案。这通过P多项式结构提供了由单变量 Krawtchouk 和双 Hahn 多项式组成的双变量正交多项式族的双谱特性（即递推关系和差分关系）。基于双谱算子的代数也与该关联方案的子构成代数一起进行了研究。