Abstract

We consider the polynomials of the form $P(x)=x^k-\gamma \mathrm{Tr}(x)$ over $\mathbb{F}_{q^n}$ for $n\geq 2$. We show that $P(x)$ is not a permutation of $\mathbb{F}_{q^n}$ in the case $\gcd(k, q^n-1)>1$. Our proof uses an absolutely irreducible curve over $\mathbb{F}_{q^n}$ and the number of rational points on it.

DOI

10.3906/mat-1811-27

Keywords

Function fields, permutation polynomials, rational places

First Page

533

Last Page

538

Recommended Citation

MEIDL, N. A (2019). Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$. Turkish Journal of Mathematics 43 (1): 533-538. https://doi.org/10.3906/mat-1811-27

Download