New Quantum MDS Codes From Negacyclic Codes

Let be an odd prime power. Based on classical negacyclic codes, we construct two classes of quantum maximum-distance-separable (MDS) codes with parameters [[q(2) + 1, q(2) - 2d + 3, d]](q) where q equivalent to 1 (mod 4) and 2 <= d <= q + 1 is even, and [[(q(2) + 1)/2, (q(2) + 1)/2 - 2d + 2, d]](q) where 3 <= d <= q is odd. Some of these quantum MDS codes are new in the sense that their parameters are different from all the previously known ones.