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Link to original content: https://doi.org/10.1007/s12095-020-00457-9
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Two families of subfield codes with a few weights

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Abstract

Subfield codes of linear codes over finite fields have recently received a lot of attention, as some of these codes are optimal and have applications in secrete sharing, authentication codes and association schemes. In this paper, two families of binary subfield codes with a few weights are presented from two special classes of linear codes, and their parameters are explicitly determined. Moreover, the parameters of the duals of these subfield codes are also studied. The two infinite families of subfield codes presented in this paper are distance-optimal with respect to the Griesmer bound and their duals are almost distance-optimal with respect to the sphere-packing bound.

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Acknowledgments

The authors are very grateful to the reviewers and the Editor, for their comments and suggestions that improved the presentation and quality of this paper. This paper was supported by the National Natural Science Foundation of China under grant numbers 11701187 and 11971175.

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Authors and Affiliations

  1. College of Mathematics and Informatics, South China Agricultural University, Guangzhou, Guangdong, 510642, China

    Can Xiang

  2. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, China

    Wenjuan Yin

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  1. Can Xiang
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  2. Wenjuan Yin
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Correspondence to Can Xiang.

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Xiang, C., Yin, W. Two families of subfield codes with a few weights. Cryptogr. Commun. 13, 117–127 (2021). https://doi.org/10.1007/s12095-020-00457-9

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  • DOI: https://doi.org/10.1007/s12095-020-00457-9

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