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A class of cyclotomic linear codes and their generalized Hamming weights

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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.

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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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Authors and Affiliations

  1. Faculty of School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, 233030, Anhui Province, People’s Republic of China

    Fei Li

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  1. Fei Li
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Correspondence to Fei Li.

Additional information

This research is supported in part by National Natural Science Foundation of China (61602342).

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Li, F. A class of cyclotomic linear codes and their generalized Hamming weights. AAECC 29, 501–511 (2018). https://doi.org/10.1007/s00200-018-0355-1

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  • DOI: https://doi.org/10.1007/s00200-018-0355-1

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