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The [1, 0]-twisted generalized Reed-Solomon code

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Abstract

In this paper, we not only give the parity check matrix of the [1, 0]-twisted generalized Reed-Solomon (in short, TGRS) code, but also determine the weight distribution. Especially, we show that the [1, 0]-TGRS code is not GRS or EGRS. Furthermore, we present a sufficient and necessary condition for any punctured code of the [1, 0]-TGRS code to be self-orthogonal, and then construct several classes of self-dual or almost self-dual [1, 0]-TGRS codes. Finally, on the basis of these self-dual or almost self-dual [1, 0]-TGRS codes, we obtain some LCD [1, 0]-TGRS codes.

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Acknowledgements

This research was supported by the National Science Foundation of China (12071321).

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Authors and Affiliations

  1. School of Computer Science and Technology, Dongguan University of Technology, 523000, Dongguan, China

    Canze Zhu

  2. College of Mathematical Science, Sichuan Normal University, 610066, Chengdu, China

    Qunying Liao

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  1. Canze Zhu
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Canze Zhu provide the idea and write the paper. Qunying liao do some check of the paper. All authors reviewed the manuscript.

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Correspondence to Qunying Liao.

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Zhu, C., Liao, Q. The [1, 0]-twisted generalized Reed-Solomon code. Cryptogr. Commun. (2024). https://doi.org/10.1007/s12095-024-00704-3

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