Permutation polynomials, fractional polynomials, and algebraic curves

2017/08/16 by Bartoli, Daniele, Giulietti, Massimo
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1708.04841

Abstract

In this note we prove a conjecture by Li, Qu, Li, and Fu on permutation trinomials over \mathbbF₃^2k. In addition, new examples and generalizations of some families of permutation polynomials of \mathbbF_3^k and \mathbbF_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.

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