Some new QEC MDS codes with large minimum distance

Abstract

Abstract The advancement of Quantum Error-Correcting (QEC) Maximum Distance Separable (MDS) codes holds substantial importance in practical applications, substantially augmenting the reliability and efficiency of quantum communication and computing. This paper introduces two new classes of QEC MDS codes, which are devised through the utilization of generalized Reed–Solomon (GRS) codes and the Hermitian construction approach. The novelty of our QEC MDS codes lies in their parameters being distinct from all previously reported codes. Moreover, most of our codes possess a considerably greater minimum distance in comparison to existing codes of the same length.