dorsal/arxiv
View SchemaQuantum Goppa Codes over Hyperelliptic Curves
| Authors | Annika Niehage |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0501074 |
| URL | https://arxiv.org/abs/quant-ph/0501074 |
Abstract
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.
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"abstract": "This Diplom thesis provides an explicit construction of a quantum Goppa code\nfor any hyperelliptic curve over a non-binary field. Hyperelliptic curves have\nconjugate pairs of rational places. We use these pairs to construct\nself-orthogonal classical Goppa codes with respect to a weighted inner product.\nThese codes are also self-orthogonal with respect to a symplectic inner product\nand therefore define quantum stabilizer codes. A final transformation leads to\na quantum Goppa code with respect to the standard symplectic inner product.\nSome examples illustrate the described construction.\n Furthermore we present a projection of a higher dimensional code onto the\nbase field and a special case when the projected code is again weighted\nself-orthogonal and symmetric.",
"arxiv_id": "quant-ph/0501074",
"authors": [
"Annika Niehage"
],
"categories": [
"quant-ph"
],
"title": "Quantum Goppa Codes over Hyperelliptic Curves",
"url": "https://arxiv.org/abs/quant-ph/0501074"
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