New Quantum MDS Codes From Negacyclic Codes

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