New Quantum MDS Codes with Flexible Parameters from Hermitian Self-Orthogonal GRS Codes

TL;DR

This paper introduces a flexible method for constructing new quantum MDS codes with diverse parameters using Hermitian self-orthogonal GRS codes, expanding the known range of quantum error-correcting codes.

Contribution

It presents a novel construction technique for quantum MDS codes based on Hermitian self-orthogonal GRS codes, allowing for more flexible code parameters.

Findings

New quantum MDS codes with previously unknown parameters

Construction method applicable for various divisors of q-1 and q+1

Enhanced flexibility in quantum code length and dimension

Abstract

Let $q$ be a prime power. Let $\lambda>1$ be a divisor of $q-1$, and let $\tau>1$ and $\rho>1$ be divisors of $q+1$. Under certain conditions we prove that there exists an MDS stabilizer quantum code with length $n=\lambda \tau \sigma$ where $2\le \sigma \le \rho$. This is a flexible construction, which includes new MDS parameters not known before.