This article is cited in 14 papers

Theoretical Foundations of Applied Discrete Mathematics

Piecewise-affine permutations of finite fields

A. D. Bugrov

Certification Research Center, Moscow, Russia

Abstract: Piecewise-affine permutations (p.-a. p.) are defined on any field $\mathrm{GF}(q)$. They are a generalization of piecewise-linear permutations firstly introduced by A. B. Evans. Here some estimates for linear characteristics of p.-a. p. on $\mathrm{GF}(q)$ are given. In some cases, their exact values are pointed. Polynomials representing p.-a. p. are described. Under some conditions on $\sqrt{q-1}$, it is proved that piecewise-affine permutations form the full symmetric group of $\mathrm{GF}(q)$.

Keywords: finite field, piecewise-linear permutations, piecewise-affine permutations, linear characteristic of permutations.

UDC: 512.624

DOI: 10.17223/20710410/30/1

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