On Euclidean Hulls Of MDS Codes

In this thesis,a special maximum distance separable(MDS)code,the Euclidean hull of the(extended)generalized Reed-Solomon((extended)GRS)code is taken into account.Firstly,some knowledge about finite field and GRS codes is given.Using these knowledge,a method for judging the codeword in the hull of(extended)GRS code is given.It is also applicable to self-orthogonal codes and self-dual codes.Next,the definition of almost self-dual is given and a special almost self-dual situation is considered in this thesis.The above judgment method is used to construct MDS code with arbitrary dimensions of Euclidean hulls.This thesis mainly constructs from the following two aspects when q>3.One is to construct the GRS codes by using the(almost)self-dual GRS codes.The other is to use the self-dual codes to construct the extended GRS codes with odd and even length respectively.And the dimension of Euclidean hulls of such codes can also be determined.It turns that our constructions are more general than previous works on Euclidean hulls of(extended)GRS codes.Simultaneously,some specific examples are given to illustrate the rationality of the construction and the specific application of the construction method.Finally,some related knowledge of quantum codes and the connection of the hull between quantum codes and classic codes are given.And the MDS codes of hulls with arbitrary dimensions are applied to construct EAQECCs.We can get some more general MDS EAQECCs.Besides,we clarify the specific application of the method of construction through some examples.