A class of cyclotomic linear codes and their generalized Hamming weights
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.
KeywordsCyclotomic linear code Generalized Hamming weight Weight distribution Gauss sum Gaussian period
Mathematics Subject Classification94B05 11T22 11T23
I explicitly acknowledge anonymous reviewers for their valuable suggestions and comments, which have helped improve the quality of the paper. I am also extremely grateful to the editors for their careful considerations and kind help.
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