Abstract
Subspace codes have important applications in random network coding. It is a classical problem to construct subspace codes where both their size and their minimum distance are as large as possible. In particular, cyclic constant dimension subspace codes have additional properties which can be used to make encoding and decoding more efficient. In this paper, we construct large cyclic constant dimension subspace codes with minimum distances \(2k-2\) and 2k. These codes are contained in \(\mathscr {G}_q(n, k)\), where \(\mathscr {G}_q(n, k)\) denotes the set of all k-dimensional subspaces of the finite filed \(\mathbb {F}_{q^n}\) of \(q^n\) elements (q a prime power). Consequently, some results in [7, 15], and [23] are extended.
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Acknowledgements
The authors deeply thank the Associate Editor and the anonymous referees for their helpful comments and valuable suggestions, improving highly the paper’s quality. The first author is grateful for the hospitality and support of the University of Paris VIII Department of Mathematics at the Laboratory LAGA, France, where she visits Professor Sihem Mesnager. This work was supported by the National Natural Science Foundation of China under Grant Nos. 12271199 and 12171191 and The Fundamental Research Funds for the Central Universities 30106220482. S. Mesnager is supported by the French Agence Nationale de la Recherche through ANR algeBrA, pRoofs, pRotocols, Algorithms, Curves and sUrfaces for coDes and their Applications (BARRACUDA) -ANR-21-CE39-0009.
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Communicated by M. Lavrauw.
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Li, Y., Liu, H. & Mesnager, S. New constructions of constant dimension subspace codes with large sizes. Des. Codes Cryptogr. 92, 1423–1437 (2024). https://doi.org/10.1007/s10623-023-01350-1
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DOI: https://doi.org/10.1007/s10623-023-01350-1