# New Quantum MDS Codes over Finite Fields

## TL;DR

This paper introduces three new classes of quantum MDS codes over finite fields, expanding the range of code lengths and achieving larger minimum distances than previously known, using Hermitian self-orthogonal Reed-Solomon codes.

## Contribution

The paper presents novel quantum MDS code constructions with flexible lengths and larger minimum distances, advancing quantum error correction capabilities.

## Key findings

- Constructed three new classes of quantum MDS codes.
- Achieved minimum distances larger than q/2+1.
- Enhanced flexibility in code lengths compared to prior work.

## Abstract

In this paper, we present three new classes of $q$-ary quantum MDS codes utilizing generalized Reed-Solomon codes satisfying Hermitian self-orthogonal property. Among our constructions, the minimum distance of some $q$-ary quantum MDS codes can be bigger than $\frac{q}{2}+1$. Comparing to previous known constructions, the lengths of codes in our constructions are more flexible.