Nonbinary Quantum Goppa codes excequantum Gilbert -Varshamov bound

Niehage, Annika

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URN: urn:nbn:de:bsz:180-madoc-17371
Document Type: Working paper
Year of publication: 2006
The title of a journal, publication series: None
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Classification: MSC: 94B65 94B60 81P68 ,
Subject headings (SWD): Goppa-Code , Quantenkryptologie , Codierung
Keywords (English): quantum error-correcting codes , coding theory , algebraic geometry
Abstract: An explicit construction for nonbinary quantum Goppa codes (often also called quantum AG codes) exceeding the quantum Gilbert-Varshamov bound is given. First a weighted symplectic inner product is introduced and a method how to transform weighted codes into quantum codes with respect to the standard symplectic inner product is given. Then families of quantum Goppa codes using a tower of function fields by Stichtenoth are constructed. Finally a proof that these codes lie above the quantum Gilbert-Varshamov bound is given.
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Das Dokument wird vom Publikationsserver der Universitätsbibliothek Mannheim bereitgestellt.

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