Two Types Of Three-weight Binary Linear Codes

The theory of error correcting code is an important branch of information theory,whose foundation is based on mathematics.The development of the theory of error correcting code comes from the requirement of the research of error control in electronic computer technology and modern communication technology.Therefore,the research on this field has been focused on not only by communication workers,but also by the mathematician.With the development of mathematics and information theory,the coding theory has been developed rapidly.The paper is focus on the construction of linear codes.With the method which people mainly uses in the construction of binary linear codes from Boolean function,we choose different functions to construct the linear codes,present the weight distribution,and research the dual codes.The main contents of this paper are as follows:Chapter 1 is the introduction,which mainly describes the background and the history of error correcting code,and some aspects of development of modern coding theory,and states research results of this dissertation at last.Chapter2 is the preparation,which mainly introduces the foundation of algebra and the theory of error correcting codes.This theoretical knowledge has laid a solid foundation for this article.Chapter3 is the main content,which mainly considers the construction of binary linear codes from Boolean function,presents three-weight binary linear codes and the weight distribution,and the parameters of the dual codes.Chapter4 is the summary,which mainly summarizes the main contents of this paper,also puts forward the new question to linear codes.