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A family of distance-optimal minimal linear codes with flexible parameters

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Abstract

Due to their wide applications in communications, data storage and cryptography, linear codes have received much attention in the past decades. The objective of this paper is to construct a family of linear codes over \({\mathbb F}_{q}\), where q is a prime power. This family of codes has length (qk − 1)t, dimension ek, where k ≥ 2 and e, t are arbitrary integers with 2 ≤ e ≤ t . In some cases, this class of linear codes is distance-optimal with respect to the Griesmer bound. The weight distribution of this family of linear codes is also determined. Furthermore, we show that our codes can be used to construct secret sharing schemes with interesting access structures and strongly regular graphs with new parameters.

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Acknowledgments

The authors are very grateful to the reviewers and the Editor for their valuable comments that improved the presentation and quality of this paper. This work was supported by the Natural Science Foundation of China, in part by Sichuan Science and Technology Program under Grant 2018JY0046 and in part by the Joint fund of the Ministry of Education of China under Grant 6141A02033349.

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Authors and Affiliations

  1. School of Mathematics, Southwest Jiaotong University, Chengdu, China

    Xia Li & Cuiling Fan

  2. College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China

    Xiaoni Du

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  1. Xia Li
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  2. Cuiling Fan
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  3. Xiaoni Du
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Correspondence to Cuiling Fan.

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Li, X., Fan, C. & Du, X. A family of distance-optimal minimal linear codes with flexible parameters. Cryptogr. Commun. 12, 559–567 (2020). https://doi.org/10.1007/s12095-019-00373-7

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