The Weight Distribution Of Binary Cyclic Codes With Length P~m

In coding theory,it is important to determine the weight distribution of codes.If we obtain the weight distribution of a code,we master the construction of the code basically.Furthermore,the minimum weight of a code has strongly relationship with its ability of error correction,therefore,the computation of weight distribu-tion of codes has attracted a lot of research interests of coding theory researchers.Especially,binary cyclic codes forms an important class of linear codes for both theoretical and practical significance.This thesis focuses on the research of weight distribution of binary cyclic codes.Generally,it is difficult to determine the weight distribution of cyclic codes.This thesis mainly discusses the weight distribution of binary cyclic codes with length pm,under the condition that the multiplicative order of 2 modulo pm is?(pm),where ?(·)is the Euler ?-function.Concretely,in Chapter 2,by modifying the method presented by Sharma et al.,the weight distribution of binary irreducible cyclic codes with length pm are obtained.In Chapter 3,utilizing the method of investigation on q-nary BCH codes with length qm-1,given by Cunsheng Ding et al.,the binary BCH codes with length pm are determined.Finally,based on above works,the minimum weights of binary cyclic codes with length pm are obtained in Chapter 4,under the condition that the multiplicative order of 2 modulo pm is ?(pm).