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

Abstract

Let $q$ be a prime power. Let $\hat{I}»>1$ be a divisor of $q-1$, and let $\ddot{I}„>1$ and $\ddot{I}>1$ be divisors of $q+1$. Under certain conditions we prove that there exists an MDS stabilizer quantum code with length $n=\hat{I}»\ddot{I}„\ddot{I}ƒ$ where $2\le \ddot{I}ƒ\le \ddot{I}$. This is a flexible construction, which includes new MDS parameters not known before.