Asymptotically good quantum codes exceeding the Ashikhmin-Litsyn-Tsfasman bound

It is known that quantum error correction can be achieved using classical binary codes or additive codes over F₄. Asymptotically good quantum codes have been constructed from algebraic-geometry codes and a bound on (δ, R) was computed from the Tsfasman-Vladut-Zink bound of the theory of classical algebraic-geometry codes. In this correspondence, by the use of a concatenation technique we construct a family of asymptotically good quantum codes exceeding the bound in a small interval