Geodesic
Piecewise-affine permutations of finite fields
Prikladnaâ diskretnaâ matematika, no. 4 (2015), pp. 5-23.

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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, linear characteristic of permutations.
Mots-clés : piecewise-affine permutations 
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A. D. Bugrov. Piecewise-affine permutations of finite fields. Prikladnaâ diskretnaâ matematika, no. 4 (2015), pp. 5-23. http://geodesic.mathdoc.fr/item/PDM_2015_4_a0/

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