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A note on the constructions of MDS self-dual codes

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Abstract

Due to the nice structures of maximum distance separable (MDS) codes and self-dual codes, it is worth studying MDS self-dual codes. It is easy to see that parameters of a MDS self-dual code are completely determined by the code length. The main problem in this topic is to determine existence of q-ary MDS self-dual codes of various lengths. The problem is completely solved when q is even. This paper focuses on the case that q is odd. We generalize the technique in [13] and construct several classes of MDS self-dual codes via generalized Reed-Solomon codes and extended generalized Reed-Solomon codes.

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Acknowledgements

The author is grateful to the editor and anonymous referees for careful reading and for many useful suggestions. The author sincerely thanks Professor Maosheng Xiong for his useful comments which improve the quality of this paper. This work was supported by National Cryptography Development Fund under Grant MMJJ20170119.

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  1. School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, China

    Haode Yan

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  1. Haode Yan
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Correspondence to Haode Yan.

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Yan, H. A note on the constructions of MDS self-dual codes. Cryptogr. Commun. 11, 259–268 (2019). https://doi.org/10.1007/s12095-018-0288-3

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  • DOI: https://doi.org/10.1007/s12095-018-0288-3

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