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

View as HTML     View as gif image    View as LaTeX source

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.

All articles are published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/97/973/97302h.htm
Last modified: January 20, 2000