Nonbinary Quantum Goppa Codes Exceeding the Quantum Gilbert-Varshamov Bound

Nonbinary Quantum Goppa Codes Exceeding the Quantum Gilbert-Varshamov Bound An explicit construction for nonbinary quantum Goppa codes exceeding the quantum Gilbert-Varshamov bound is given. First, we introduce a weighted symplectic inner product and show a method how to transform weighted codes into quantum codes with respect to the standard symplectic inner product. Then an algorithm to construct a quantum code out of any hyperelliptic curve is presented and implemented in Magma. Finally, we apply a generalization of this algorithm to a tower of function fields by Stichtenoth and show that these codes lie above the quantum Gilbert-Varshamov bound. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Nonbinary Quantum Goppa Codes Exceeding the Quantum Gilbert-Varshamov Bound

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Publisher
Kluwer Academic Publishers-Plenum Publishers
Copyright
Copyright © 2006 by Springer Science+Business Media, LLC
Subject
Physics; Characterization and Evaluation of Materials; Computer Science, general ; Engineering, general; Mathematics, general; Physics, general
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-006-0047-9
Publisher site
See Article on Publisher Site

Abstract

An explicit construction for nonbinary quantum Goppa codes exceeding the quantum Gilbert-Varshamov bound is given. First, we introduce a weighted symplectic inner product and show a method how to transform weighted codes into quantum codes with respect to the standard symplectic inner product. Then an algorithm to construct a quantum code out of any hyperelliptic curve is presented and implemented in Magma. Finally, we apply a generalization of this algorithm to a tower of function fields by Stichtenoth and show that these codes lie above the quantum Gilbert-Varshamov bound.

Journal

Quantum Information ProcessingSpringer Journals

Published: Dec 12, 2006

References

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