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Nonbinary quantum error-correcting codes from algebraic curves. (English) Zbl 1141.94015
The authors give a new exposition and proof of a nonbinary version of the generalized binary CSS construction. Using this construction and algebraic curves they obtain various parameters (lengths, dimensions, and minimum distances) for nonbinary quantum codes. Furthermore, they apply this construction to the tower of function fields to obtain asymptotically good nonbinary quantum codes which are constructible in polynomial time (the question of asymptotically good nonbinary quantum codes has not been considered until now).

MSC:
94B60 Other types of codes
94B27 Geometric methods (including applications of algebraic geometry) applied to coding theory
81P68 Quantum computation
14G50 Applications to coding theory and cryptography of arithmetic geometry
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