New quantum MDS codes - Zhang, Guanghui (2015)
In this paper, we construct two classes of new quantum maximum-distance-separable (MDS) codes with parameters [[ (q2 -1)/4 ,(q2 -1)/4- 2d + 2,d]]q, where q is an odd prime power with q=3 (mod 4) and 2<= d <=(3q -1) / 4 ; [[8(q -1); 8(q- 1) -2d+2, d]]q, where q is an odd prime power with the form q = 8t- 1 (t is an even positive integer) and 2<= d<= (q+15)/ 2 . Compared the parameters with all known quantum MDS codes, the quantum MDS codes exhibited here have minimum distances bigger than the ones available in the literature.