New Galois Hulls of GRS Codes and Application to MDS EAQECCs

In this paper, we construct some new (extended) generalized Reed-Solomon (GRS) codes with arbitrary dimensions of Galois hulls. For some special cases, we propose a mechanism. Precisely, these special classes of GRS codes with Galois hulls of arbitrary dimensions can be constructed from GRS codes satisfying Euclidean orthogonal property. Finally, we construct several new families of MDS entanglement-assisted quantum error-correcting codes (EAQECCs) utilizing the above GRS codes with Galois hulls of arbitrary dimensions.