Two Classes of Quantum MDS Codes with Large Minimal Distance

TL;DR

This paper constructs two new classes of quantum MDS codes with large minimal distances using finite field structures and Hermitian self-orthogonality, achieving parameters not previously reported.

Contribution

It introduces novel quantum MDS codes with larger minimal distances by leveraging multiplicative structures and Hermitian self-orthogonality in finite fields.

Findings

Codes with minimal distance larger than q/2

Parameters of these codes are novel and previously unreported

Construction method using Hermitian self-orthogonal Reed-Solomon codes

Abstract

In this paper, two classes of quantum MDS codes are constructed. The main tools are multiplicative structures on finite fields. Carefully choosing different cosets can make the corresponding generalized Reed-Solomon codes Hermitian self-orthogonal, which yields quantum MDS codes by utilizing Hermitian type CSS construction. In some cases, these codes have minimal distances larger than $q/2$. Also, the parameters of these codes have never been reported before.