In this paper we prove a conjecture by Li, Qu, Li, and Fu on permutation trinomials over $F_{3^{2k}}$. In addition, new examples and generalizations of some families of permutation polynomials of $F_{3^k}$ and $F_{5^k}$ are given. We also study permutation quadrinomials of type $Ax^{q(q−1)+1}+Bx^{2(q−1)+1}+Cx^q+x$. Our method is based on the investigation of an algebraic curve associated with a fractional polynomial over a finite field.
Permutation polynomials, fractional polynomials, and algebraic curves
Bartoli, Daniele
;Giulietti, Massimo
2018
Abstract
In this paper we prove a conjecture by Li, Qu, Li, and Fu on permutation trinomials over $F_{3^{2k}}$. In addition, new examples and generalizations of some families of permutation polynomials of $F_{3^k}$ and $F_{5^k}$ are given. We also study permutation quadrinomials of type $Ax^{q(q−1)+1}+Bx^{2(q−1)+1}+Cx^q+x$. Our method is based on the investigation of an algebraic curve associated with a fractional polynomial over a finite field.File in questo prodotto:
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