Turkish Journal of Mathematics
DOI
10.3906/mat-1811-27
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.
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
