Discrete Functions

On the curvature of one class of functions over residue rings taking binary values

O. V. Kamlovskii, S. A. Kuzmin


Abstract: We consider the class of functions $f:\mathbb{Z}_{m}\setminus\{0\}\to \{0,1\}$ for which we can obtain logarithmic estimates for the sums of the absolute values of the spectral coefficients. This class contains functions with small amount of changing of $0$ and $1$ series in their tables of values, and also functions that are linear equivalent to mentioned ones. We have determined the number of elements in that class, it equals $ m\varphi (m)+\varphi (m)( m(m-3)-1 )/2$, and suggested the algorithm for checking that a function belongs to the considered class. The results obtained will be useful for estimations of frequency characteristics of the output sequences of binary complications of linear recurring sequences.

Keywords: residue rings, estimations of trigonometric sums, Vinogradov sums.

UDC: 512.552.18

DOI: 10.17223/2226308X/18/12