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The minimum distance of new generalisations of the punctured binary Reed-Muller codes

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Abstract

In 2018, Ding et al. introduced a new generalisation of the punctured binary Reed-Muller codes to construct LCD codes and 2-designs. They studied the minimum distance of the codes and proposed an open problem about the minimum distance. In this paper, several new results on the minimum distance of the generalised punctured binary Reed- Muller are presented. Particularly, some of the results are a generalisation or improvement of previous results in (Finite Fields Appl. 53, 144–174, 2018).

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Acknowledgements

The authors are very grateful to the reviewers for their comments that improved the quality of this paper.

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Authors and Affiliations

  1. School of Cyberspace, Hangzhou Dianzi University, Hangzhou, 310018, China

    Liqin Hu

  2. Department of Mathematical Science, Tsinghua University, Beijing, 100084, China

    Keqin Feng

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  1. Liqin Hu
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  2. Keqin Feng
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Correspondence to Liqin Hu.

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The research was supported by the National Natural Science Foundation of China (Nos. 61602144, 11471178, 11571107 )

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Hu, L., Feng, K. The minimum distance of new generalisations of the punctured binary Reed-Muller codes. Cryptogr. Commun. 12, 795–808 (2020). https://doi.org/10.1007/s12095-019-00421-2

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  • DOI: https://doi.org/10.1007/s12095-019-00421-2

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