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This article studies the Hamming distances and association schemes of orthogonal arrays. We present a general method of constructing mixed schematic saturated orthogonal arrays of strength two produced from saturated symmetric orthogonal arrays by using the expansive replacement method. As applications of the method, we obtain many new mixed schematic saturated orthogonal arrays. Some examples are given to illustrate this construction method. [ABSTRACT FROM AUTHOR]

We consider the algebraic combinatorics of the set of injections from a $k$ -element set to an $n$ -element set. In particular, we give a new combinatorial formula for the spherical functions of the Gelfand pair $(S_{k} \times S_{n}, diag(S_{k}) \times S_{n-k})$. We use this combinatorial formula to give new Delsarte linear programming bounds on the size of codes over injections. [ABSTRACT FROM AUTHOR]

This paper presents a general method of constructing schematic saturated orthogonal arrays of strength two. We consider a class of mixed saturated orthogonal arrays produced from saturated symmetric orthogonal arrays by using the contractive replacement method, study the Hamming distances of the rows, construct their association schemes, and prove that they are schematic. Some examples are given to illustrate this construction method. [ABSTRACT FROM AUTHOR]