Quantum Goppa Codes over Hyperelliptic Curves [article]

Annika Niehage
2005 arXiv   pre-print
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
more » ... 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.
arXiv:quant-ph/0501074v1 fatcat:2eoxnuw7dzcphoafkgybmj6nzq