Two new classes of quantum MDS codes from generalized Reed-Solomon codes

Abstract

In this paper, we mainly use classical Hermitian self-orthogonal generalized Reed-Solomon codes to construct two new classes of quantum MDS codes. Most of our quantum MDS codes have minimum distance larger than q/2+1. Compared with previously known constructions, these quantum MDS codes in our constructions have large minimum distance and their parameters are not covered by the previous codes.

Unfortunately, we have recognized that the quantum MDS codes in our manuscript is covered by the codes in the reference [17]. We are going to rearrange this manuscript and try to give more new results