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New Constructions of Orbit Codes Based on the Operations of Orbit Codes

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Abstract

An orbit code is a special constant dimension subspace code, which is an orbit of a subgroup of a general linear group acting on the set of all subspaces in the given ambient space. This paper presents some methods of constructing new orbit codes from known orbit codes. Firstly, we introduce the sum operation, intersection operation and union operation of subspace codes, and then we give some methods to obtain new orbit codes from known orbit codes by fully applying the sub-orbits of permutation groups and the direct product operation of the groups. Finally, as a special application, partial spread codes are researched and a condition of orbit codes with constant distance is given.

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Acknowledgments

We wish to thank the editor and the referees for their valuable comments which enhanced the presentation of this paper.

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Authors and Affiliations

  1. College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Shang-di Chen

  2. Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Jun-ying Liang

Authors
  1. Shang-di Chen
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  2. Jun-ying Liang
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Correspondence to Shang-di Chen.

Additional information

This paper is supported by the Fundamental Research Funds of the Central Universities of China Civil Aviation University of Key Projects of Natural Science (No. 3122019192).

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Chen, Sd., Liang, Jy. New Constructions of Orbit Codes Based on the Operations of Orbit Codes. Acta Math. Appl. Sin. Engl. Ser. 36, 803–815 (2020). https://doi.org/10.1007/s10255-020-0974-8

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  • DOI: https://doi.org/10.1007/s10255-020-0974-8

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