On Quantum MDS Codes - Roetteler, Martin; Grassl, Markus; Beth, Thomas (International Symposium om Information Theory, 2004. ISIT 2004., 2004)
We construct maximum distance separable quantum error-correcting codes. The codes are defined over q-dimensional quantum systems, where q is any prime power. The construction yields quantum MDS codes of length up to q+1 for all possible dimensions and some quantum MDS codes of length up to q2+1. In particular, those families contain codes [[6,2,3]]p and [[7,3,3]]p for pges3 (cf. [K. Feng (2002)]).