Construction of quantum MDS codes from generalized Reed–Solomon codes.

Quantum maximum-distance-separable (MDS) codes play an important role in the quantum codes. The previous quantum MDS codes had been constructed according to q is odd or even. However, such classification omits to consider some special categories of quantum MDS codes. Because of this, we will discuss the other classifications of q. In this paper, we construct some new q -ary quantum MDS codes from generalized Reed–Solomon codes by using Hermitian construction, and prove that these quantum MDS codes have minimum distance greater than q 2 , where q ≡ − 1 (mod 3). [ABSTRACT FROM AUTHOR]