Theoretical Foundations of Applied Discrete Mathematics

Necessary and sufficient conditions of linear structure triviality for monomial mapping on the field of $2^{2^t}$ elements

A. N. Alekseychuk, R. V. Proskurovskiy

Institute of Special Communications and Protection of Informatics, National Technical University of Ukraine "Kiev Polytechnic Institute", Kiev, Ukraine

Abstract: The necessary and sufficient conditions are obtained in terms of binary structure of natural number $d$, under which all non-zero linear combinations of coordinate functions of mapping $x\mapsto x^d$, $x\in\mathbf{GF}(2^{2^t})$, don't have linear translators.

Keywords: linear structure of discrete mappings, finite field, monomial mapping.

UDC: 519.95