Orthogonal systems of polynomials in finite fields

Abstract

The notion of an orthogonal system of polynomials in several variables in finite fields is introduced which generalizes a concept of orthogonality by Kurbatov and Starkov. Necessary and sufficient conditions for orthogonality in terms of character sums and permutation polynomials are given. Results of Carlitz on systems of equations in finite fields and earlier results of the author on permutation polynomials in several variables are generalized.