On optimal quantum codes
Quantum Physics
2023-11-27 v1 Emerging Technologies
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.
Cite
@article{arxiv.quant-ph/0312164,
title = {On optimal quantum codes},
author = {Markus Grassl and Thomas Beth and Martin Roetteler},
journal= {arXiv preprint arXiv:quant-ph/0312164},
year = {2023}
}
Comments
Accepted for publication in the International Journal of Quantum Information