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Two-to-one mappings and involutions without fixed points over F2n
Finite Fields and Their Applications ( IF 1 ) Pub Date : 2021-08-25 , DOI: 10.1016/j.ffa.2021.101913 Mu Yuan 1 , Dabin Zheng 1 , Yan-Ping Wang 2
中文翻译:
F2n 上无不动点的二对一映射和对合
更新日期:2021-08-25
Finite Fields and Their Applications ( IF 1 ) Pub Date : 2021-08-25 , DOI: 10.1016/j.ffa.2021.101913 Mu Yuan 1 , Dabin Zheng 1 , Yan-Ping Wang 2
Affiliation
In this paper, two-to-one mappings and involutions without any fixed point on finite fields of even characteristic are investigated. First, we characterize a closed relationship between them by implicit functions and develop an AGW-like criterion for 2-to-1 mappings. Using this criterion, some new constructions of 2-to-1 mappings are proposed and eight classes of 2-to-1 mappings of the form are obtained. Finally, a number of classes of involutions without any fixed point are derived from the known 2-to-1 mappings by the relation between them.
中文翻译:
F2n 上无不动点的二对一映射和对合
本文研究了偶特征有限域上无不动点的二一映射和对合。首先,我们通过隐函数来表征它们之间的封闭关系,并为 2 对 1 映射开发了类似 AGW 的标准。使用这个标准,提出了一些新的 2 对 1 映射结构和八类形式的 2 对 1 映射获得。最后,通过它们之间的关系,从已知的 2 对 1 映射导出了许多没有任何不动点的对合类。