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On Euclidean Hulls of MDS Codes

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Abstract

In this paper, we propose a mechanism for the construction of MDS codes with arbitrary dimensions of Euclidean hulls. Precisely, we construct (extended) generalized Reed-Solomon (GRS) codes with assigned dimensions of Euclidean hulls from self-orthogonal GRS codes. It turns out our constructions are more general than previous works on Euclidean hulls of (extended) GRS codes.

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Acknowledgements

The authors thank anonymous reviewers and the editor for their suggestions and comments to improve the readability of this paper. This research is supported by National Natural Science Foundation of China under Grant 11471008, Grant 11871025 and the self-determined research funds of CCNU from the colleges’ basic research and operation of MOE(Grant No. CCNU18TS028). This work is also supported by the Fundamental Research Funds for the Central Universities (Innovation Funding Project) under Grant 2019CXZZ075.

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  1. Xiaolei Fang

    Present address: School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan, 430048, China

Authors and Affiliations

  1. School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, China

    Xiaolei Fang, Meiqing Liu & Jinquan Luo

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  1. Xiaolei Fang
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  2. Meiqing Liu
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  3. Jinquan Luo
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Correspondence to Jinquan Luo.

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Fang, X., Liu, M. & Luo, J. On Euclidean Hulls of MDS Codes. Cryptogr. Commun. 13, 1–14 (2021). https://doi.org/10.1007/s12095-020-00428-0

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  • DOI: https://doi.org/10.1007/s12095-020-00428-0

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