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A class of cyclotomic linear codes and their generalized Hamming weights (1708.04415v1)
Published 15 Aug 2017 in cs.IT, math.IT, and math.NT
Abstract: 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.