Asymptotic bounds on quantum codes from algebraic geometry codes

Abstract

We generalize a characterization of p-ary (p is a prime) quantum codes given by Feng and Xing to q-ary (q is a prime power) quantum codes. This characterization makes it possible to convert an asymptotic bound of Stichtenoth and Xing for nonlinear algebraic geometry codes to a quantum asymptotic bound. Besides, we also investigate the asymptotic behavior of quantum codes