FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

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 $\mathbb{Z}/k$ 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 $\mathbb{Z}/4$ 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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