A construction of combinatorial arrays from non-linear functions

Abstract

Bose [2] proposed a construction of orthogonal arrays. The construction uses linear transformations over a finite field. Fuji-Kara and Miyamoto [3] generalized this method by considering non-linear functions in stead of linear transformations and constructed combinatorial arrays such as orthogonal arrays and balanced arrays. In particular, we constructed combinatorial arrays by using quadratic functions over finite fields of even prime power orders. In this paper, we construct combinatorial arrays for odd prime power orders. Moreover we give some constructions of balanced arrays as an application of the results obtained here.