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Journal of Applied Mathematics and Computing

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22.03.2019 | Original Research

Rank-metric complementary dual codes

verfasst von: Xiusheng Liu, Hualu Liu

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2019

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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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Titel: Rank-metric complementary dual codes
verfasst von: Xiusheng Liu
Hualu Liu
Publikationsdatum: 22.03.2019
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2019
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-019-01254-1

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