Construction Of GRS Codes With Specific Dimension Hull

In this thesis,we construct two new classes of Euclidean self-orthogonal codes from criterions for e-Galois self-orthogonal codes.The first class is[p4e,pe,p4e-pe+1]q-MDS code constructed by GRSpe(a,v).We fix n=p4e and choose a vector a-(a1,…,an),which {a1,…,an}=Fp4e.The second class is[p2e,pe,p2e-pe+2]q-MDS code constructed by GRSpe(a,1,?).We fix n=P2e and choose a vector a=(a1,…,an),which {a1,…,an}=Fp2e.We also proved these two MDS codes are e-Galois self-orthogonal codes.In Chapter 4,we give three types of e-Galois hulls of GRS codes with specific dimensions.Firstly,we construct two Euclidean self-orthogonal GRS codes from two criterions of Euclidean self-orthogonal GRS codes.Then we construct two e-Galois hull of GRS codes with specific dimensions from two self-orthogonal GRS codes,which obtained by two criterions of Euclidean self-orthogonal GRS codes.The first class e-Galois hull of GRSk(a,v')code with l dimen-sions,which 0 ?l ?k?[Pe+n-1/pe+1],construct from[n,m]q Euclidean self-orthogonal GRS codes.The second class e-Galois hull of GRSk(a,v',?)code with l dimensions,which 0 ?l ?k-1 and k?[pe+n-1/pe+1],construct from[n+1,m]q Euclidean self-orthogonal GRS codes.Finally,we construct a class of e-Galois hull[p2e+1,pe]q MDS code with l dimensional,which 0?l?pe,from the criterion of e-Galois self-orthogonal GRS codes.