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A class of cyclotomic linear codes and their generalized Hamming weights

Original Paper

Abstract

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.

Keywords

Cyclotomic linear code Generalized Hamming weight Weight distribution Gauss sum Gaussian period 

Mathematics Subject Classification

94B05 11T22 11T23 

Notes

Acknowledgements

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of School of Statistics and Applied MathematicsAnhui University of Finance and EconomicsBengbuPeople’s Republic of China

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