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