On optimal quantum codes
<|reference_start|>On optimal quantum codes: 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.<|reference_end|>
@article{grassl2003on,
    title={On optimal quantum codes},
    author={Markus Grassl (Universitaet Karlsruhe),, Thomas Beth (Universitaet
  Karlsruhe), and Martin Roetteler (University of Waterloo)},
    journal={International Journal of Quantum Information, Vol. 2, No. 1
  (2004), pp. 55-64},
    year={2003},
    doi={10.1142/S0219749904000079},
    archivePrefix={arXiv},
    eprint={quant-ph/0312164},
    primaryClass={quant-ph cs.ET}
}