On Quantum MDS Codes

  • Martin Roetteler ,
  • Markus Grassl ,
  • Thomas Beth

International Symposium om Information Theory, 2004. ISIT 2004. |

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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)]).