New Classes of Entanglement-assisted Quantum MDS Codes

TL;DR

This paper introduces two new classes of entanglement-assisted quantum MDS codes with improved parameters, expanding the known options for quantum error correction over finite fields.

Contribution

The paper presents novel constructions of EAQMDS codes with lengths dividing q^2-1 and q^2+1, including many with unprecedented parameters and larger minimum distances.

Findings

Many new EAQMDS codes with previously unreported parameters

Some codes exhibit significantly larger minimum distances

The constructions cover lengths dividing q^2-1 and q^2+1

Abstract

In this paper, we produce two new classes of entanglement-assisted quantum MDS codes (EAQMDS codes) with length $n|q^2-1$ and $n|q^2+1$ via cyclic codes over finite fields of odd characteristic. Among our constructions there are many EAQMDS codes with new parameters which have never been reported. And some of them have great larger minimum distance than known results.