FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1997, VOLUME 3, NUMBER 3, PAGES 653-674

Approximation of k-ary functions by functions from the given system

A. S. Ambrosimov

Abstract

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Problems of k-ary functions approximation by functions from the given system are investigated in this paper. In particular, generalization of Golomb theorem is obtained in the case of ring Z/k or finite field GF(q). The definition of k-ary functions equivalency with respect to the given functions system is introduced. Classes of equivalency with respect to the linear functions system over finite field or ring Z/4 are described. Limit theorems on cardinality of random k-ary functions equivalency class are proved. Also in this paper we found functions which minimize maximum probability of coincidence with linear functions in one variable over finite ring with identity.


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