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A family of linear codes from constant dimension subspace codes

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Abstract

Linear codes with good parameters have wide applications in secret sharing schemes, authentication codes, association schemes, consumer electronics and communications, etc. During the past four decades, constructions of linear codes with good parameters received much attention and many classes of such codes were presented. In this paper, we obtain a family of linear codes with good parameters over \(\mathbb {F}_p\) by exploring further properties of constant dimension subspace codes, where p is a prime. The weight distribution of three classes of linear codes presented in this family is determined. Most notably, three classes of linear codes presented in this family are distance-optimal with respect to the Griesmer bound. Also, this paper presents a sufficient and necessary condition for this family of linear codes to have a \(\lambda \)-dimensional hull. In addition, we show that our linear codes can be used to construct secret sharing schemes with interesting access structures and strongly regular graphs.

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Acknowledgements

We wish to thank the anonymous reviewers and the editors for their insightful and instructive suggestions that improved the technical as well as editorial quality of this paper. This work was supported in part by the National Natural Science Foundation of China (Nos. 61872435, 62172219, 61772015, 12031011), the National Key R&D Program of China (No. 2020YFA0712300), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. SJKY\(19_{-}0167\)).

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Authors and Affiliations

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

    Xia Li & Qin Yue

  2. Science and Technology on Communication Security Laboratory, Chengdu, 610041, Sichuan, People’s Republic of China

    Xia Li & Deng Tang

  3. State Key Laboratory of Cryptology, P. O. Box 5159, Beijing, 100878, People’s Republic of China

    Qin Yue

  4. School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Deng Tang

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  1. Xia Li
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  2. Qin Yue
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  3. Deng Tang
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Correspondence to Deng Tang.

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Communicated by C. Ding.

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The paper was supported by National Natural Science Foundation of China (No. 61772015), the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. SJKY\(19_{-}0167\))

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Li, X., Yue, Q. & Tang, D. A family of linear codes from constant dimension subspace codes. Des. Codes Cryptogr. 90, 1–15 (2022). https://doi.org/10.1007/s10623-021-00960-x

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  • DOI: https://doi.org/10.1007/s10623-021-00960-x

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