The Complete Weight Distributions Of A Class Of Cyclic Codes

Cyclic codes are a spcial class of linear codes with good algebraic structure and properties,which have been widely used in communication and storage systems.In recent decades,the complete weight distributions of cyclic codes have been extensively studied by scholars.The weight distribution of a code can be obtained from its complete weight distribution.The information of the complete weight distribution of a code is of vital use in practical applications.The complete weight distribution of a code can be applied to study monomial and quadratic bent functions.Also,it has an important application in the construction of optimal constant composition codes.Let p be an odd prime,m and l be positive integers with m ? 2,1 ?l?m-1,? be a primitive element of Fpm.In this thesis,we determine the complete weight distributions of a class of cyclic codes over Fp with parity-check polynomi-al h1(x)h2(x)h3(x),where h1(x),h2(x)and h3(x)are the minimal polynomials of?-1,?-2 and ?-(pl+1)over Fp,respectively.