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Nonbinary Quantum Goppa Codes Exceeding the Quantum Gilbert-Varshamov Bound
Authors:Annika Niehage
Affiliation:1.Fakult?t für Mathematik und Informatik,Universit?t Mannheim,Mannheim,Germany
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.
Keywords:quantum error-correcting codes  coding theory  algebraic geometry
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