New Quantum MDS Codes From Negacyclic Codes

Let q be an odd prime power. Based on classical negacyclic codes, we construct two classes of quantum maximum-distance-separable (MDS) codes with parameters [[q²+1, q²-2d+3, d]]q where q ≡ 1 (mod 4) and 2 ≤ d ≤ q+1 is even, and [[(q²+1)/2,(q²+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.