Cyclic codes and some new entanglement-assisted quantum MDS codes

TL;DR

This paper introduces four new families of entanglement-assisted quantum MDS codes with flexible lengths and larger minimum distances, expanding the available quantum error correction options.

Contribution

The authors present novel EAQMDS codes with a more general length and a new method for selecting defining sets, achieving larger minimum distances than previous codes.

Findings

Four new families of EAQMDS codes with flexible lengths

Codes have larger minimum distances than existing ones

All constructed codes are new and not covered by prior literature

Abstract

Entanglement-assisted quantum error correcting codes (EAQECCs) play a significant role in protecting quantum information from decoherence and quantum noise. Recently, constructing entanglement-assisted quantum maximum distance separable (EAQMDS) codes with flexible parameters has received much attention. In this work, four families of EAQMDS codes with a more general length are presented. And the method of selecting defining set is different from others. Compared with all the previously known results, the EAQMDS codes we constructed have larger minimum distance. All of these EAQMDS codes are new in the sense that their parameters are not covered by the quantum codes available in the literature.