  This Diplom thesis provides an explicit construction of a quantum Goppa code
for any hyperelliptic curve over a non-binary field. Hyperelliptic curves have
conjugate pairs of rational places. We use these pairs to construct
self-orthogonal classical Goppa codes with respect to a weighted inner product.
These codes are also self-orthogonal with respect to a symplectic inner product
and therefore define quantum stabilizer codes. A final transformation leads to
a quantum Goppa code with respect to the standard symplectic inner product.
Some examples illustrate the described construction.
  Furthermore we present a projection of a higher dimensional code onto the
base field and a special case when the projected code is again weighted
self-orthogonal and symmetric.
