Approximation of restrictions of q-valued logic functions to linear manifolds by affine analogues

Abstract

Abstract For a finite q-element field Fq, we established a relation between parameters characterizing the measure of affine approximation of a q-valued logic function and similar parameters for its restrictions to linear manifolds. For q > 2, an analogue of the Parseval identity with respect to these parameters is proved, which implies the meaningful upper estimates qn−1(q − 1) − qn/2−1 and qr−1(q − 1) − qr/2−1, for the nonlinearity of an n-place q-valued logic function and of its restrictions to manifolds of dimension r. Estimates characterizing the distribution of nonlinearity on manifolds of fixed dimension are obtained.