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Further improvement on index bounds

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Abstract

In this paper we obtain further improvement of index bounds for character sums of polynomials over finite fields. We present some examples, which show that our new bound is an improved bound compared to both the Weil bound and the index bound given by Wan and Wang. As an application, we give an estimation of the number of all the solutions of some algebraic curves by using our result.

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Acknowledgements

The authors thank the anonymous reviewers for their helpful suggestions.

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Authors and Affiliations

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

    Yansheng Wu

  2. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, People’s Republic of China

    Yansheng Wu

  3. Department of Mathematics, Ewha Womans University, Seoul, 03760, Republic of Korea

    Yoonjin Lee

  4. School of Mathematics and Statistics, Carleton University, Ottawa, ON, K1S 5B6, Canada

    Qiang Wang

Authors
  1. Yansheng Wu
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  2. Yoonjin Lee
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  3. Qiang Wang
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Corresponding author

Correspondence to Yoonjin Lee.

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Communicated by This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue: On Coding Theory and Combinatorics: In Memory of Vera Pless”.

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Y. Wu was sponsored by the National Natural Science Foundation of China (Grant No. 12101326) and the Natural Science Foundation of Jiangsu Province (Grant No. BK20210575). .

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Wu, Y., Lee, Y. & Wang, Q. Further improvement on index bounds. Des. Codes Cryptogr. 90, 2813–2821 (2022). https://doi.org/10.1007/s10623-021-00987-0

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  • DOI: https://doi.org/10.1007/s10623-021-00987-0

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