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An improvement on Weil bounds for character sums of polynomials over finite fields

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Abstract

Let \(\mathbb {F}_q\) be a finite field with q elements, where q is a power of a prime p. In this paper, we obtain an improvement on Weil bounds for character sums associated to a polynomial f(x) over \(\mathbb {F}_q \), which extends the results of Wan et al. (Des. Codes Cryptogr. 81, 459–468, 2016) and Wu et al. (Des. Codes Cryptogr. 90, 2813–2821, 2022).

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Acknowledgements

The authors are very grateful to the reviewers and the Editor for their valuable suggestions that much improved the quality of this paper.

Funding

The paper was supported by National Natural Science Foundation of China under Grants 12171420, 62172219, 12271059, Natural Science Foundation of Shandong Province under Grant ZR2021MA046, Natural Science Research Start up Foundation of Recruiting Talents of Nanjing University of Posts and Telecommunications (Grant No.NY223199), and the Fundamental Research Funds for the Central Universities, CHD, under Grant 300102122202.

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Authors and Affiliations

  1. College of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, People’s Republic of China

    Fengwei Li

  2. School of Mathematics and Statistics, Zaozhuang University, Zaozhuang, 277160, People’s Republic of China

    Fanhui Meng

  3. School of Science, Chang’an University, Xi’an, 710064, People’s Republic of China

    Ziling Heng

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

    Qin Yue

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  1. Fengwei Li
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  2. Fanhui Meng
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  3. Ziling Heng
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  4. Qin Yue
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Contributions

F. Li and F. Meng wrote the main manuscript text and Z. Heng and Q. Yue gave examples. All authors reviewed the manuscript.

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Correspondence to Fengwei Li.

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Li, F., Meng, F., Heng, Z. et al. An improvement on Weil bounds for character sums of polynomials over finite fields. Cryptogr. Commun. (2024). https://doi.org/10.1007/s12095-024-00706-1

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