Mathematics, Department of
Date of this Version
7-2008
Citation
Published in Discrete Math, 308 (2008), pp 3115-3124.
doi 10.1016/j.disc.2007.08.038
Abstract
We give a generalized CSS construction for nonbinary quantum error-correcting codes. Using this we construct nonbinary quantum stabilizer codes from algebraic curves. We also give asymptotically good nonbinary quantum codes from a Garcia- Stichtenoth tower of function fields which are constructible in polynomial time.
Binary quantum error-correcting codes have been constructed in several ways. One interesting construction uses algebraic-geometry codes [2], [6], [7], [12], with the main idea being to apply the binary CSS construction [4], [5], [16] to the asymptotically good algebraic-geometry codes arising from the Garcia-Stichtenoth [11] tower of function fields over Fq2 (where q is a power of 2) attaining the Drinfeld-Vladut bound [17].
It is natural to consider nonbinary quantum codes. Beyond the simple fact that nonbinary error-correcting codes are interesting in the classical case, Rains [14] points out that there are indeed applications in which nonbinary quantum codes would be more appropriate than binary quantum codes. Though nonbinary quantum codes have been considered in [1], [3], [9], [14], the majority of attention has been given thus far to the binary case. In particular, the question of asymptotically good nonbinary quantum codes has not been studied until now.
Comments
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