Quantum generalized Reed-Solomon codes: Unified framework for quantum MDS codes

Details Quantum generalized Reed-Solomon codes: Unified framework for quantum MDS codes Quantum generalized Reed-Solomon codes: Unified framework for quantum MDS codes

2008-12-24

arxiv.org/abs/0812.4514v1

Phys. Rev. A, 2008, 77, 012308

Physics

Quantum Physics

9 pages, no figures

Scientific paper

10.1103/PhysRevA.77.012308

We construct a new family of quantum MDS codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them analytically. We find that existing quantum MDS codes can be unified under these codes in the sense that when a quantum MDS code exists, then a quantum code of this type with the same parameters also exists. Thus as far as is known at present, they are the most important family of quantum MDS codes.

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