幂置换的Boomerang一致性与上的代数曲线𝔽2n

IF 0.5 4区 数学 Q3 MATHEMATICS
Sihem Mesnager, F. Özbudak
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引用次数: 0

摘要

得到了F2n $F(x)={{x}^{{{2}^{m}}-1}}\text{ }\!\!~\!\!\text{ of }\!\!~\!\!\text{ }{{\mathbb{F}}_{{{2}^{n}}}}$中m∈{3,n−12,n+12,n−2的幂置换F(x)=x2m−}1的回旋连通性表。$\left\{ 3,\frac{n-1}{2},\frac{n+1}{2},n-2 \right\}.$特别地,我们得到了F(x)在b∈F2n∈F2处的Boomerang均匀性和Boomerang均匀性集。$F(x)\text{ }\!\!~\!\!\text{ at }\!\!~\!\!\text{ }b\in {{\mathbb{F}}_{{{2}^{n}}}}\setminus {{\mathbb{F}}_{2}}.$此外,我们还利用F2n上某些具体代数曲线的有理点数确定了F(x)的完整回旋镖分布谱。${{\mathbb{F}}_{{{2}^{n}}}}.$我们还明确地确定了回飞镖均匀性的分布谱。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Boomerang uniformity of power permutations and algebraic curves over 𝔽2n
Abstract We obtain the Boomerang Connectivity Table of power permutations F(x)=x2m−1 of F2n $F(x)={{x}^{{{2}^{m}}-1}}\text{ }\!\!~\!\!\text{ of }\!\!~\!\!\text{ }{{\mathbb{F}}_{{{2}^{n}}}}$with m ∈ { 3,n−12,n+12,n−2 }. $\left\{ 3,\frac{n-1}{2},\frac{n+1}{2},n-2 \right\}.$In particular, we obtain the Boomerang uniformity and the Boomerang uniformity set of F(x) at b∈F2n∖F2. $F(x)\text{ }\!\!~\!\!\text{ at }\!\!~\!\!\text{ }b\in {{\mathbb{F}}_{{{2}^{n}}}}\setminus {{\mathbb{F}}_{2}}.$Moreover we determine the complete Boomerang distribution spectrum of F(x) using the number of rational points of certain concrete algebraic curves over F2n. ${{\mathbb{F}}_{{{2}^{n}}}}.$We also determine the distribution spectra of Boomerang uniformities explicitly.
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来源期刊
Advances in Geometry
Advances in Geometry 数学-数学
CiteScore
1.00
自引率
0.00%
发文量
31
审稿时长
>12 weeks
期刊介绍: Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.
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