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On optimal quantum codes

Markus Grassl·Thomas Beth·Martin Roetteler
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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.

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Markus Grassl, Thomas Beth, Martin Roetteler. 2003-12-19. On optimal quantum codes. https://doi.org/10.1142/s0219749904000079

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