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A class of subfield codes of linear codes and their duals

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Abstract

Recently, subfield codes of some optimal linear codes have been studied. In this paper, we further investigate a class of subfield codes and generalize the results of the subfield codes of the conic codes in Ding and Wang (Finite Fields Appl. 56, 308–331, 2020). The weight distributions of these subfield codes and the parameters of their duals are determined. Some of the presented codes are optimal or almost optimal according to Grassl (2020) and their duals are distance-optimal with respect to the Sphere Packing bound if p > 3. As a byproduct, we directly obtain the weight distributions of the punctured codes, which is the same with the results presented in Du et al. (2019a, b), and determine the parameters of the duals of the punctured codes. These dual codes are distance-optimal with respect to the Sphere Packing bound with rare exceptions.

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Acknowledgments

The authors sincerely thank the reviewers and the editor for their helpful comments and valuable suggestions, which have improved the presentation of this paper. This work was partially supported by National Natural Science Foundation of China under Grants 11971156, 12001175 and 61977021, and Hubei province science and technology innovation major project under Grant 2019ACA144.

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Authors and Affiliations

  1. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China

    Xiaoqiang Wang & Dabin Zheng

  2. School of Computer Science and Information Engineering, Hubei University, Wuhan, 430062, China

    Yan Zhang

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  1. Xiaoqiang Wang
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  2. Dabin Zheng
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  3. Yan Zhang
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Correspondence to Dabin Zheng.

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Wang, X., Zheng, D. & Zhang, Y. A class of subfield codes of linear codes and their duals. Cryptogr. Commun. 13, 173–196 (2021). https://doi.org/10.1007/s12095-020-00460-0

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