A Class Of Two-Weight And Three-Weight Linear Codes Over Finite Fields Of Odd Characteristic

Linear codes have applications in communication,data storage,authentication codes,strongly regular graphs and secret sharing schemes,so the construction of linear codes has attracted the attentions of many scholars.In this paper,a class of two-weight and threeweight linear codes is obtained by the defining sets determined by the bivariate functions over finite fields of odd characteristic.The parameters and weight distributions of linear codes are determined by the additive characters,multiplicative characters and Gauss sums.Further,most of linear codes obtained are minimal,which can be used to construct secret sharing schemes.The organization structure of this paper is as follows.The first chapter is the introduction.This chapter introduces the background and application of linear codes,and focuses on the research status of linear codes with few weights.Finally,the main content of this paper is summarized.The second chapter is preliminary knowledge.This chapter mainly introduces some basic knowledge of finite fields,trace mappings,Gauss sums,exponential sums and secret sharing scheme.This theoretical knowledge has built a solid foundation for this paper.The third chapter constructs a class of two-weight linear codes,and the parameters and weight distributions of this class of linear codes are determined by using Gauss sums and exponential sums.The fourth chapter constructs a class of three-weight linear codes,and the parameters and weight distributions of this class of linear codes are determined by using Gauss sums and exponential sums.The last chapter is the summary and expectation.