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Construction of constant dimension codes via improved inserting construction

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Constant dimension codes (CDCs), as special subspace codes, have attracted extensive attention due to their application at random network coding. In this paper, we present some variations on the insert construction method by changing the positions of some matrices. Those variations help us to construct more types of CDCs. By restricting the rank of matrices in rank metric codes, We can get that the union of these codes is still a CDC and the minimum subspace distance can be preserved. We generalize the previous results in He et al. (IEEE Commun Lett 25(5):1422–1426, 2021) and Lao et al. (arXiv:2008.09944v1, 2020) and obtain some new lower bounds of CDCs.

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Funding

The paper is supported by National Natural Science Foundation of China (Nos. 61772015, 62172219), the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX20-0226).

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Authors and Affiliations

  1. School of Computer Science and Artificial Intelligence, Changzhou University, Changzhou, 213164, People’s Republic of China

    Yongfeng Niu

  2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, People’s Republic of China

    Qin Yue

  3. College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, People’s Republic of China

    Daitao Huang

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  1. Yongfeng Niu
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  2. Qin Yue
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  3. Daitao Huang
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Correspondence to Yongfeng Niu.

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Niu, Y., Yue, Q. & Huang, D. Construction of constant dimension codes via improved inserting construction. AAECC 34, 1045–1062 (2023). https://doi.org/10.1007/s00200-021-00537-0

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  • DOI: https://doi.org/10.1007/s00200-021-00537-0

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