Two new classes of quantum MDS codes

Let p be a prime and let q be a power of p. In this paper, by using generalized Reed-Solomon (GRS for short) codes and extended GRS codes, we construct two new classes of quantum maximum-distance-separable (MDS) codes with parameters[[tq,tq−2d+2,d]]q for any 1≤t≤q,2≤d≤⌊tq+q−1q+1⌋+1, and[[t(q+1)+2,t(q+1)−2d+4,d]]q for any 1≤t≤q−1,2≤d≤t+2 with (p,t,d)≠(2,q−1,q). Our quantum MDS codes have flexible parameters, and have minimum distances larger than q2+1 when t>q2. Furthermore, it turns out that our constructions generalize and improve some previous results.