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Some t-designs from BCH codes

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Abstract

Combinatorial t-designs are closely related to coding theory and finite geometries and have nice applications in some engineering areas. One of the major approaches to the construction of combinatorial t-designs is the employment of error-correcting codes. In this paper, this approach is further investigated with a class of linear codes related to the extended BCH codes and their duals over finite fields. By determining the parameters of these codes, an infinite family of 3-designs is presented and their parameters are also explicitly determined. In addition, the parameters of some combinatorial 2-designs from the extended codes of certain primitive BCH codes are also determined. Moreover, Research Problem 9.4 proposed by Ding in [Designs from Linear Codes, World Scientific, Singapore, pp: 257, 2018)] is also solved.

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Acknowledgements

The author is very grateful to the reviewers and the Editor, for their comments and suggestions that improved the presentation and quality of this paper. This paper was supported by the Basic Research Project of Science and Technology Plan of Guangzhou city of China under grant number 202102020888, and the National Natural Science Foundation of China under grant numbers 12171162, 11701187 and 11971175.

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  1. College of Mathematics and Informatics, South China Agricultural University, Guangzhou, Guangdong, 510642, China

    Can Xiang

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  1. Can Xiang
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Correspondence to Can Xiang.

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Xiang, C. Some t-designs from BCH codes. Cryptogr. Commun. 14, 641–652 (2022). https://doi.org/10.1007/s12095-021-00546-3

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  • DOI: https://doi.org/10.1007/s12095-021-00546-3

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