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More classes of permutation pentanomials over finite fields with characteristic two

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成果类型:
期刊论文
作者:
Zhang, Tongliang;Zheng, Lijing;Zhao, Hanbing
通讯作者:
Zheng, LJ
作者机构:
[Zhao, Hanbing; Zhang, Tongliang] North China Univ Sci & Technol, Coll Sci, Tangshan 063000, Hebei, Peoples R China.
[Zheng, Lijing] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构:
[Zheng, LJ ] U
Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
语种:
英文
关键词:
Finite field;Niho exponent;Permutation pentanomial
期刊:
Finite Fields and Their Applications
ISSN:
1071-5797
年:
2024
卷:
98
页码:
102468
基金类别:
Na- tional Natural Science Foundation of China [62372221]; Basic research expenses of colleges and universities in Hebei Province Research Project [JQN2022002]
机构署名:
本校为通讯机构
院系归属:
数理学院
摘要:
Let q = 2 m . In this paper, we investigate permutation pentanomials over F q 2 of the form f ( x ) = x t + x r 1 ( q − 1 ) + t + x r 2 ( q − 1 ) + t + x r 3 ( q − 1 ) + t + x r 4 ( q − 1 ) + t with gcd ( x r 4 + x r 3 + x r 2 + x r 1 + 1 , x t + x t − r 1 + x t − r 2 + x t − r 3 + x t − r 4 ) = 1 . We transform the problem concerning permutation property of f ( x ) into demonstrating that the corresponding fractional polynomial permutes the unit circle U of F q 2 with order q + 1 via a well-known lemma, and then into showing that there...

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