The classifications of o-monomials and of 2-to-1 binomials are equivalent

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-30 DOI:10.1007/s10623-024-01463-1

Lukas Kölsch, Gohar Kyureghyan

引用次数: 0

Abstract

We observe that on the binary finite fields the classification of 2-to-1 binomials is equivalent to the classification of o-monomials, which is a well-studied and elusive problem in finite geometry. This connection implies a complete classification of 2-to-1 binomials \(b=x^d+ux^e\) for a large set of values of (d, e). Further, we show that a number of the known infinite families of 2-to-1 maps can be traced back to o-polynomials or to difference maps of APN maps. We also provide some connections between 2-to-1 maps and hyperovals in non-desarguesian planes.

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邻单项式和 2 对 1 二项式的分类是等价的

我们观察到，在二元有限域上，2-to-1 二项式的分类等同于邻单项式的分类，而邻单项式的分类是有限几何中一个研究得很透彻而又难以捉摸的问题。这种联系意味着对于大量的 (d, e) 值集，2-to-1 二项式的完整分类是 \(b=x^d+ux^e/)。此外，我们还证明了一些已知的 2 对 1 映射无穷族可以追溯到邻多项式或 APN 映射的差映射。我们还提供了 2 到 1 映射与非德萨格平面中的超ovals 之间的一些联系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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