Weight And Complete Weight Distributions Of A Class Of Linear Codes

The weight analysis of linear codes has always been an important topic in error correction coding.The weight and complete weight distributions of linear error correcting codes not only describe the error correcting ability of codes,but also help to analyze and calculate the errors in the process of information transmission.In recent years,the application of linear codes with less weight in the fields of secret key sharing,strong regular graph,combination scheme and authentication code has attracted many scholars' extensive research.Let F_p~m be a finite field of size p~m,p be odd prime,m,k and l be positive integers.In this paper,we investigate linear codeswhereBy using the theory of quadratic forms over finite fields and some special Weil sums,we determine the weight enumerator and the complete weight enumerator of this kind of linear codes.This paper generalizes some results in [26,47,53].The parameters and weight distributions of the punctured codes of the discussed linear codes are also determined,and some optimal codes with respect to the Griesmer bound and some strongly regular graphs from two-weight projective codes are obtained.