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A new construction of cyclic subspace codes

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Abstract

Subspace codes have attracted a lot of attention in the last few decades due to their applications in noncoherent linear network coding, in particular cyclic subspace codes can be encoded and decoded more efficiently because of their special algebraic structure. In this paper, we present a family of cyclic subspace codes with minimum distance \(\varvec{2k-2}\) and size \(\varvec{seq^{k}(q^k-1)^{s-1}(q^n-1)+\frac{q^n-1}{q^k-1}}\), where \(\varvec{k|n}\), \(\varvec{\frac{n}{k}\ge 2s+1}\), \(\varvec{s\ge 1, e=\lceil \frac{n}{2sk} \rceil -1}\). In the case of \(\varvec{n=(2s+1)k}\) with \(\varvec{2\le s <q^k}\), our cyclic subspace codes have larger size than the known ones in the literature.

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Acknowledgements

The authors are very grateful to the editor and the anonymous referees for their helpful comments and suggestions which improved the quality of the paper.

Funding

This work was supported by National Natural Science Foundation of China under Grant No. 12171241 and No. 12226408, and Natural Science Foundation of Jiangsu Province, Grant No. BK20230867.

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Authors and Affiliations

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

    Yuqing Han & Xiwang Cao

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

    Xiwang Cao

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  1. Yuqing Han
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Correspondence to Xiwang Cao.

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Han, Y., Cao, X. A new construction of cyclic subspace codes. Cryptogr. Commun. 16, 1527–1537 (2024). https://doi.org/10.1007/s12095-024-00735-w

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