Preprint A553/2007
On additive polynomials and certain maximal curves

Saeed Tafazolian | Garcia, Arnaldo

**Keywords: **
finite fields | maximal curves | additive polynomials | exponential sums

We show that a maximal curve over $\FF _{q^{2}}$ given by an
equation $A(X)=F(Y)$, where $A(X) \in \FF _{q^{2}}[X]$ is additive and separable and where $F(Y) \in \FF _{q^{2}}[Y]$ has degree $m$ prime to the characteristic $p$, is such that all roots of $A(X)$ belong to $\FF _{q^{2}}$.
In the particular case where $F(Y)=Y^{m}$, we show that the degree $m$ is a divisor of $q+1$.