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Designs, Codes and Cryptography

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28.01.2020

Full classification of permutation rational functions and complete rational functions of degree three over finite fields

verfasst von: Andrea Ferraguti, Giacomo Micheli

Erschienen in: Designs, Codes and Cryptography | Ausgabe 5/2020

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Abstract

Let q be a prime power, \(\mathbb {F}_q\) be the finite field of order q and \(\mathbb {F}_q(x)\) be the field of rational functions over \(\mathbb {F}_q\). In this paper we classify and count all rational functions \(\varphi \in \mathbb {F}_q(x)\) of degree 3 that induce a permutation of \(\mathbb {P}^1(\mathbb {F}_q)\). As a consequence of our classification, we can show that there is no complete permutation rational function of degree 3 unless \(3\mid q\) and \(\varphi \) is a polynomial.

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Titel: Full classification of permutation rational functions and complete rational functions of degree three over finite fields
verfasst von: Andrea Ferraguti
Giacomo Micheli
Publikationsdatum: 28.01.2020
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 5/2020
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-020-00715-0

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