Quantum Generalized Reed-Solomon codes

Abstract

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.