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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 toarXiv:quant-ph/0501074v1 fatcat:2eoxnuw7dzcphoafkgybmj6nzq