A polynomial-time construction of self-orthogonal codes and applications to quantum error correction

Abstract

A polynomial-time construction of a sequence of self-orthogonal geometric Goppa codes attaining the Tsfasman-Vlăduţ-Zink (TVZ) bound is presented. The issue of constructing such a code sequence was addressed in a context of constructing quantum error-correcting codes (Ashikhmin et al., 2001). Naturally, the obtained construction has implications on quantum error-correcting codes. In particular, the best known asymptotic lower bounds on the largest minimum distance of polynomially constructible quantum error-correcting codes are improved.