量子Generalized Reed-Solomon码

Quantum Generalized Reed-Solomon codes

构造出了一族量子纠错码,这族码具有参数[[n,n-2k,k+1]]q,是q维量子系统上的码,q是任意素数的幂.这族码的最小距离达到了理论上限,因此,以码距来说,它是最优的.证明了当2≤n≤q或者q2-q+2≤n≤q2时,码都是存在的.

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 q^2-q＋2≤n≤q^2.