Some New Constructions of Quantum MDS Codes

TL;DR

This paper introduces six new classes of q-ary quantum MDS codes using GRS codes and Hermitian construction, achieving larger minimum distances and longer lengths than previous codes, thus advancing quantum error correction capabilities.

Contribution

Six new classes of quantum MDS codes are constructed with improved parameters, extending the range and performance of quantum error correction codes.

Findings

Minimum distances larger than q/2+1

Longer code lengths than previous constructions

Improved minimum distances for some known codes

Abstract

It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes of q-ary quantum MDS codes by using generalized Reed-Solomon (GRS) codes and Hermitian construction. The minimum distances of our quantum MDS codes can be larger than q/2+1 Three of these six classes of quantum MDS codes have longer lengths than the ones constructed in [1] and [2], hence some of their results can be easily derived from ours via the propagation rule. Moreover, some known quantum MDS codes of specific lengths can be seen as special cases of ours and the minimum distances of some known quantum MDS codes are also improved as well.