The Weight Distribution Of Some Classes Of Linear Codes And The Separation Of A Binary Relative Constant-weight Code

Recently,by using defining set,linear codes with a few weights have been extensive-ly constructed and studied due to their applications to secret sharing,authentication codes and strongly regular graphs.In the first part of this paper,we generalize the code constructed recently by Wang et al,and obtain many classes of codes with a few weights.The weight distribution and the minimum distance of the duals of these codes are completely determined.We also show that some subclasses of the duals of these codes are optimal.Furthermore,some parameters of the generalized Hamming weight of these codes are calculated in certain cases.In the second part,several classes of linear codes with a few weights over the finite field F_pare constructed for an odd prime p by choosing defining set properly,and the complete weight enumerators of these classes of codes are determined.In the third part,certain formulas for computing the minimum values of the cardinality of separating coordinate position of the codeword sets are pre-sented for any binary linear code.With the above formulas,this paper determine the separation of any codeword sets of a binary relative constant-weight code in terms of code parameters.