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Letqbe 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]]qwhereq≡ 1 (mod 4) and 2 ≤d≤q+1 is even, and [[(q2+1)/2,(q2+1)/2-2d+2,d]]qwhere 3 ≤d≤qis odd. Some of these quantum MDS codes are new in the sense that their parameters are different from all the previously known ones.
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Kai et al. (2012) studied this question.
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