Quantum Goppa Codes over Hyperelliptic Curves

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dc.creatorNiehage, Annika
dc.date2005-01-14
dc.date.accessioned2026-07-07T06:11:57Z
dc.date.available2026-07-07T06:11:57Z
dc.descriptionThis 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.
dc.description93 pages
dc.identifierhttps://arxiv.org/abs/quant-ph/0501074
dc.identifierhttp://arxiv.org/abs/quant-ph/0501074
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/92645
dc.subjectQuantum Physics
dc.titleQuantum Goppa Codes over Hyperelliptic Curves
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