  It is well known that the Gauss map for a complex plane curve is birational,
whereas the Gauss map in positive characteristic is not always birational. Let
$q$ be a power of a prime integer. We study a certain plane curve of degree
$q^2+q+1$ for which the Gauss map is inseparable with inseparable degree $q$.
As a special case, we show a relation between the dual curve of the Fermat
curve of degree $q^2+q+1$ and the Ballico-Hefez curve.
