Two new classes of quantum MDS codes
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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-1/q+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 codes have flexible parameters, and have minimum distances larger than q/2+1 when t > q/2. Furthermore, it turns out that our constructions generalize and improve some previous results.
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