A class of cyclotomic linear codes and their generalized Hamming weights

摘要

Firstly, we give a formula on the generalized Hamming weights of linear codes constructed generically by defining sets. Secondly, by choosing properly the defining set we obtain a class of cyclotomic linear codes and then present two alternative formulas for calculating their generalized Hamming weights. Lastly, we determine their weight distributions and generalized Hamming weights partially. Especially, we solve the generalized Hamming weights completely in one case.