Two-to-one mappings and involutions without fixed points over $\bF_{2^n}$

Mu Yuan; Dabin Zheng; Yanping Wang

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arXiv · 2105.11323

Two-to-one mappings and involutions without fixed points over $\bF_{2^n}$

Mu Yuan·Dabin Zheng·Yanping Wang

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Abstract

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 $(x^{2^k}+x+\delta)^{s}+cx$ 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.

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Mu Yuan, Dabin Zheng, Yanping Wang. 2021-05-24. Two-to-one mappings and involutions without fixed points over $\bF_{2^n}$. https://arxiv.org/abs/2105.11323

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