Product is universal for the class of linear functions over Galua field

Recieved: 06/12/2025

Accepted: 06/20/2025

Keywords: generation, universal function, polinomial, Galua field.

To cite this article

Voronenko A.A., Selyankina E.A. Product is universal for the class of linear functions over Galua field. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2025. N 4, p.13-16 https://doi.org/10.55959/MSU/0137–0782–15–2025–49–4–13–16.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Voronenko A.A. (Lomonosov Moscow State University (MSU))
Selyankina E.A. (Lomonosov Moscow State University (MSU))

Abstract

It was proved earlier that product xy is a universal function for the class of linear functions depending on two arguments if k=6l±1. Then the criterion of existence of a universal polinomial was obtained for any number of arguments and any k. In this paper we show that product xy is universal for any class of linear functions over Galua field GF(p^m), where p is any prime and m is natural, m⩾2.