Two Classes Of Linear Codes And Their Weight Distributions

Linear codes have been a popular issue in the research of coding,for which is a important part of error-correcting codes.The weight distribution of linear code identi-fies its error-correcting capacity.Researching the weight distributions of linear codes could also improves the efficiency of decoding linear codes.Linear code with few weights have applications in secret sharing,authentication codes,association schemes,and strongly regular graphs,in addition to their applications in consumer electronics,communication and data storage system.Study the weight distributions of linear codes has significant meaning in both academic and application prospects.In this paper,we use defining sets to give the linear codes to be studied:We chose two kinds of quadratic functions to define two classes of sets Used to construct two classes of linear codes.This paper proves that the linear codes have two or three weights and gives their weight distributions by quadratic form.