@article{grassl2003on, author = {Grassl, Markus and Beth, Thomas and Roetteler, Martin}, title = {On Optimal Quantum Codes}, year = {2003}, month = {December}, abstract = {We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary prime power. It is shown that codes with parameters [[n,n-2d+2,d]]_q exist for all 3 <= n <= q and 1< = d <= n/2+1. We also present quantum MDS codes with parameters [[q^2,q^2-2d+2,d]]_q for 1 <= d <= q which additionally give rise to shortened codes [[q^2-s,q^2-2d+2-s,d]]_q for some s.}, url = {http://approjects.co.za/?big=en-us/research/publication/optimal-quantum-codes/}, pages = {55-64}, journal = {International Journal of Quantum Information}, }