New quantum MDS codes

Abstract

In this paper, we construct two classes of new quantum maximum-distance-separable (MDS) codes with parameters [Formula: see text], where q is an odd prime power with q ≡ 3 (mod 4) and [Formula: see text]; [[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 [Formula: see text]. Comparing 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.