  Firstly, we give a formula on the generalized Hamming weight 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 to calculate their generalized Hamming weights. Lastly, we
determine their weight distribution and generalized Hamming weights partially.
Especially, we solved the generalized Hamming weights completely in one case.
