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.
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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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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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Li, F., Meng, F., Heng, Z. et al. An improvement on Weil bounds for character sums of polynomials over finite fields. Cryptogr. Commun. 16, 879–887 (2024). https://doi.org/10.1007/s12095-024-00706-1
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DOI: https://doi.org/10.1007/s12095-024-00706-1