Turkish Journal of Mathematics
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, NURDAGÜL ANBAR
(2019)
"Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$,"
Turkish Journal of Mathematics: Vol. 43:
No.
1, Article 43.
https://doi.org/10.3906/mat-1811-27
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss1/43
