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We construct a family of quantum error-correcting codes with parameters ［［n，n-2k，k+1］］q which are defined in q-dimensional quantum systems，where q is an arbitrary prime power. These codes are optimal in the sense that the minimum distance is maximal. It is shown that codes exist for all n satisfying 2≤n≤q or q2-q+2≤n≤q2.
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Keywords:
- quantum Generalized Reed-Solomon codes /
- quantum MDS codes /
- quantum error-correcting codes /
- quantum information
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