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Weight distributions and weight hierarchies of a family of p-ary linear codes

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Abstract

The weight distribution and weight hierarchy of a linear code are two important research topics in coding theory. In this paper, by choosing proper defining sets from inhomogeneous quadratic functions over \({\mathbb {F}}_{q}^{2}\), we construct a family of three-weight p-ary linear codes and determine their weight distributions and weight hierarchies. Most of the codes can be used in secret sharing schemes.

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Acknowledgements

The authors are very grateful to the reviewers and the editors, for their comments and suggestions that improved the presentation and quality of this paper.

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Authors and Affiliations

  1. Faculty of School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, 233041, Anhui, People’s Republic of China

    Fei Li

  2. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, People’s Republic of China

    Xiumei Li

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  1. Fei Li
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Correspondence to Xiumei Li.

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Communicated by V. A. Zinoviev.

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The research was supported by Anhui Provincial Natural Science Foundation No. 1908085MA02 and the National Science Foundation of China Grant Nos. 12001312 and 11701001.

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Li, F., Li, X. Weight distributions and weight hierarchies of a family of p-ary linear codes. Des. Codes Cryptogr. 90, 49–66 (2022). https://doi.org/10.1007/s10623-021-00962-9

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