Date of this Version
Published in Discrete Math, 308 (2008), pp 3115-3124.
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 , , , , with the main idea being to apply the binary CSS construction , ,  to the asymptotically good algebraic-geometry codes arising from the Garcia-Stichtenoth  tower of function fields over Fq2 (where q is a power of 2) attaining the Drinfeld-Vladut bound .
It is natural to consider nonbinary quantum codes. Beyond the simple fact that nonbinary error-correcting codes are interesting in the classical case, Rains  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 , , , , 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.