The Galois hulls of linear codes are a generalization of the Euclidean and
Hermitian hulls of linear codes. In this paper, we study the Galois hulls of
(extended) GRS codes and present several new constructions of MDS codes with
Galois hulls of arbitrary dimensions via (extended) GRS codes. Two general
methods of constructing MDS codes with Galois hulls of arbitrary dimensions by
Hermitian or general Galois self-orthogonal (extended) GRS codes are given.
Using these methods, some MDS codes with larger dimensions and Galois hulls of
arbitrary dimensions can be obtained and relatively strict conditions can also
lead to many new classes of MDS codes with Galois hulls of arbitrary
dimensions.Comment: 21 pages,5 table