Nonbinary Quantum Goppa codes excequantum Gilbert -Varshamov bound

Niehage, Annika

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URL:	http://ub-madoc.bib.uni-mannheim.de/1737
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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BASE: Niehage, Annika

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