Several families of MDS QECCs and MDS EAQECCs from Hermitian self-orthogonal GRS codes

Maximum distance separable (MDS) quantum error-correcting codes (QECCs) and MDS entanglement-assisted QECCs (EAQECCs) play significant roles in quantum information theory. In this paper, we construct several new families of MDS QECCs and MDS EAQECCs by utilizing Hermitian self-orthogonal generalized Reed–Solomon codes. These newly obtained MDS QECCs contain some known classes of MDS QECCs as subclasses and some of them have larger minimum distance. In addition, many q-ary MDS QECCs and MDS EAQECCs in our constructions have length exceeding \(q+1\) $q+1$ and minimum distance surpassing \(\frac{q}{2}+1\) $\frac{q}{2}+1$ .