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

摘要

We construct a new family of quantum MDS codes from classical generalizedReed-Solomon codes and derive the necessary and sufficient condition underwhich these quantum codes exist. We also give code bounds and show how toconstruct them analytically. We find that existing quantum MDS codes can beunified 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 asfar as is known at present, they are the most important family of quantum MDScodes.