  A problem of current interest, also motivated by applications to Coding
theory, is to find explicit equations for \textit{maximal} curves, that are
projective, geometrically irreducible, non-singular curves defined over a
finite field $\mathbb{F}_{q^2}$ whose number of $\mathbb{F}_{q^2}$-rational
points attains the Hasse-Weil upper bound of $q^2+2\mathfrak{g}q+1$ where
$\mathfrak{g}$ is the genus of the curve $\mathcal{X}$. For curves which are
Galois covered of the Hermitian curve, this has been done so far ad hoc, in
particular in the cases where the Galois group has prime order and also when
has order the square of the characteristic. In this paper we obtain explicit
equations of all Galois covers of the Hermitian curve with Galois group of
order $dp$ where $p$ is the characteristic of $\mathbb{F}_{q^2}$ and $d$ is
prime other than $p$. We also compute the generators of the Weierstrass
semigroup at a special $\mathbb{F}_{q^2}$-rational point of some of the curves,
and discuss some possible positive impacts on the minimum distance problems of
AG-codes.
