Affiliation:
1. NP “GST” , Moscow , Russia
Abstract
Abstract
For a finite q-element field F
q
, 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 q
n−1(q − 1) − q
n/2−1 and q
r−1(q − 1) − q
r/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.
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics
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