Permutations involving squares in finite fields

Hai-Liang Wu; Li-Yuan Wang; Hai-Liang Wu; Li-Yuan Wang

doi:10.3934/era.2022106

Electronic Research Archive

2022, Volume 30, Issue 6: 2109-2120. doi: 10.3934/era.2022106

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Research article

Permutations involving squares in finite fields

Hai-Liang Wu ¹,
Li-Yuan Wang ^{2
,
,}

1.
School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
2.
School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing 211816, China

Received: 12 August 2021 Revised: 28 December 2021 Accepted: 30 December 2021 Published: 14 April 2022

Let $ p $ be an odd prime and let $ \mathbb{F}_p $ be the finite field of $ p $ elements. In 2019, Sun studied some permutations involving squares in $ \mathbb{F}_p $. In this paper, by the theory of local fields we generalize this topic to $ \mathbb{F}_{p^2} $, which gives a partial answer to the question posed by Sun.
- quadratic residues,
- permutations,
- primitive roots,
- local fields
Citation: Hai-Liang Wu, Li-Yuan Wang. Permutations involving squares in finite fields[J]. Electronic Research Archive, 2022, 30(6): 2109-2120. doi: 10.3934/era.2022106

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Abstract

Let $ p $ be an odd prime and let $ \mathbb{F}_p $ be the finite field of $ p $ elements. In 2019, Sun studied some permutations involving squares in $ \mathbb{F}_p $. In this paper, by the theory of local fields we generalize this topic to $ \mathbb{F}_{p^2} $, which gives a partial answer to the question posed by Sun.

References

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