Two-to-one mappings and involutions without fixed points over $\bF_{2^n}$
Information Theory
2021-05-27 v2 math.IT
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 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.
Keywords
Cite
@article{arxiv.2105.11323,
title = {Two-to-one mappings and involutions without fixed points over $\bF_{2^n}$},
author = {Mu Yuan and Dabin Zheng and Yanping Wang},
journal= {arXiv preprint arXiv:2105.11323},
year = {2021}
}