Several Classes of New MDS Codes with Arbitrary-Dimensional Hulls and Their Applications

Hulls of linear codes have a vital effect in coding theory. Arbitrary-dimensional hull and one-dimensional hull are helpful for the construction of EAQECCs and determining the complexity of some algorithms etc., respectively. In this paper, we present some constructions from generalized Reed-Solomn codes and extend generalized Reed-Solomn codes, and determine the dimension of their hulls. Then, we get five new MDS codes with new parameters and we also give a more systematic and convenient method to construct two classes of codes that have already appeared before. And finally, we construct EAQECCs and EAQMDS codes using five classes of these seven MDS codes with arbitrary hulls, and the remaining two classes have one-dimensional hulls.