- Turkish Journal of Mathematics
- Vol: 43 Issue: 1
- Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$
Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$
Authors : Nurdagül Anbar Meidl
Pages : 533-538
View : 8 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
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