  Let $\X$ be an algebraic curve of genus $g \geq 2$ defined over a field
$\F_q$ of characteristic $p > 0$. From $\X$, under certain conditions, we can
construct an algebraic geometry code $C$. If the code $C$ is self-orthogonal
under the symplectic product then we can construct a quantum code $Q$, called a
QAG-code. In this paper we study the construction of such codes from curves
with automorphisms and the relation between the automorphism group of the curve
$\X$ and the codes $C$ and $Q$.
