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On pseudorandom subsets in finite fields I: measure of pseudorandomness and support of Boolean functions

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Abstract

Subsets with “good” properties in finite fields are widely applied in coding and cryptography. In this paper we introduce pseudorandom measures for subsets in finite fields and prove lower bounds for the pseudorandom measure. The pseudorandom properties of support of some Boolean functions are studied and the properties of cyclotomic classes in finite fields have also been discussed.

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Acknowledgements

The authors express their gratitude to the referee for his/her helpful and detailed comments.

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Authors and Affiliations

  1. School of Mathematics, Northwest University, Shaanxi, Xi’an, 710127, People’s Republic of China

    Huaning Liu & Xiaolin Chen

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  1. Huaning Liu
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  2. Xiaolin Chen
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Correspondence to Huaning Liu.

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This work is supported by National Natural Science Foundation of China under Grant No. 11571277, and the Science and Technology Program of Shaanxi Province of China under Grant No. 2019JM-573 and 2020JM-026.

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Liu, H., Chen, X. On pseudorandom subsets in finite fields I: measure of pseudorandomness and support of Boolean functions. Period Math Hung 83, 204–219 (2021). https://doi.org/10.1007/s10998-021-00380-3

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  • DOI: https://doi.org/10.1007/s10998-021-00380-3

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