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Rank-metric complementary dual codes

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Abstract

In this paper, we investigate the rank-metric codes which are proposed by Delsarte and Gabidulin to be complementary dual codes. We first point out the relationship between Delsarte complementary dual codes (Delsarte LCD codes) and Gabidulin complementary dual codes (Gabidulin LCD codes). We then construct two classes of Gabidulin LCD MRD codes by self-dual basis (or almost self-dual basis) of the finite field \(\mathbb {F}_{q^{m}}\) over base field \(\mathbb {F}_{q}\). Finally, we give an interesting application of rank-metric LCD codes in decoding algorithm.

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Acknowledgements

The authors would like to sincerely thank the editor and the referees for very meticulous readings of this paper, and for valuable suggestions which help us to create an improved version. The authors also thank Dr. Jian Bai for many helpful discussion. This research was supported by Research Funds of Hubei Province (Grant Nos. D20144401 and Q20174503), and Research Project of Hubei Polytechnic University (Grant No. 17xjz03A).

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  1. School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, 435003, China

    Xiusheng Liu & Hualu Liu

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  1. Xiusheng Liu
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Liu, X., Liu, H. Rank-metric complementary dual codes. J. Appl. Math. Comput. 61, 281–295 (2019). https://doi.org/10.1007/s12190-019-01254-1

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  • DOI: https://doi.org/10.1007/s12190-019-01254-1

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