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 [[ q 2 +1, q 2 -2 d +3, d ]] q where q ≡ 1 (mod 4) and 2 ≤ d ≤ q +1 is even, and [[( q 2 +1)/2,( q 2 +1)/2-2 d +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.