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Generalized block inserting for constructing new constant dimension codes

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Abstract

Constant dimension codes (CDCs) have drawn extensive attention due to their applications in random network coding. A fundamental problem for CDCs is to explore the maximum possible cardinality Aq(n,d,k) of a set of k-dimensional subspaces in \(\mathbb {F}^{n}_{q}\) such that the subspace distance statisfies dis(U,V ) = 2k − 2 dim(U ∩ V ) ≥ d for all pairs of distinct subspaces U and V in this set. In this paper, by means of an appropriate combination of the matrix blocks from rank metric codes and small CDCs, we present three constructions of CDCs based on the generalized block inserting construction by Niu et al. in 2021. According to our constructions, we obtain 28 new lower bounds for CDCs which are better than the previously known lower bounds.

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Acknowledgements

The authors would like to thank the anonymous referees for their carefully reading and helpful suggestions which improved the quality of the paper. This research is supported by National Natural Science Foundation of China under Grant Nos: 11771007, 12171241.

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  1. Xiwang Cao

    Present address: College of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

Authors and Affiliations

  1. College of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

    Xiaoqin Hong

  2. Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA), MIIT, Nanjing, 211106, China

    Xiwang Cao

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  1. Xiaoqin Hong
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  2. Xiwang Cao
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Correspondence to Xiwang Cao.

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Hong, X., Cao, X. Generalized block inserting for constructing new constant dimension codes. Cryptogr. Commun. 15, 1–15 (2023). https://doi.org/10.1007/s12095-022-00590-7

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  • DOI: https://doi.org/10.1007/s12095-022-00590-7

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