A recursive construction of permutation polynomials over F_(q~2) with odd characteristic related to Redei functions

Fu Shihui; Feng Xiutao; Lin Dongdai; Wang Qiang

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A recursive construction of permutation polynomials over F_(q~2) with odd characteristic related to Redei functions

机译：与REDEI功能相关的F_（Q〜2）递归结构的递归施工施加多项式

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摘要

In this paper, we construct two classes of permutation polynomials over Fq2 with odd characteristic closely related to rational Redei functions. Two distinct characterizations of their compositional inverses are also obtained. These permutation polynomials can be generated recursively. As a consequence, we can generate permutation polynomials with an arbitrary number of terms in a very simple way. Moreover, several classes of permutation binomials and trinomials are given. With the help of a computer, we find that the number of permutation polynomials of these types is quite big.

机译：在本文中，我们通过与Rational Redei功能密切相关的奇数特性构建了两种置换多项式。还获得了其组成逆的两个不同的表征。可以递归地生成这些置换多项式。结果，我们可以以非常简单的方式产生具有任意数量的术语的排列多项式。此外，给出了几种置换二项式和三组。在计算机的帮助下，我们发现这些类型的排列多项式的数量非常大。

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来源
《Designs, Codes and Crytography》 |2019年第7期|1481-1498|共18页
作者
Fu Shihui; Feng Xiutao; Lin Dongdai; Wang Qiang;
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作者单位

Chinese Acad Sci Key Lab Math Mechanizat Acad Math & Syst Sci Beijing 100190 Peoples R China;

Chinese Acad Sci Key Lab Math Mechanizat Acad Math & Syst Sci Beijing 100190 Peoples R China|Sci & Technol Commun Secur Lab Chengdu 610041 Sichuan Peoples R China;

Chinese Acad Sci Inst Informat Engn State Key Lab Informat Secur Beijing 100093 Peoples R China;

Carleton Univ Sch Math & Stat Ottawa ON K1S 5B6 Canada;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Finite fields; Permutation polynomials; Compositional inverse; Redei functions; Dickson polynomials;

机译：有限田地;排列多项式;组成逆;REDEI功能;迪克逊多项式;

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专利

1. A recursive construction of permutation polynomials over F_(q~2) with odd characteristic related to Redei functions [J] . Fu Shihui, Feng Xiutao, Lin Dongdai, Designs, Codes and Crytography . 2019,第7期

机译：与Redei函数有关的具有奇特征的F_（q〜2）上置换多项式的递归构造
2. The compositional inverse of a class of linearized permutation polynomials over F_(2~n),n odd [J] . Baofeng Wu Finite fields and their applications . 2014,第sepa期

机译：F_（2〜n），n奇数上一类线性置换多项式的成分逆
3. New constructions of permutation polynomials of the form x~rh (x~(q-1)) over F_(q~2) [J] . Li Kangquan, Qu Longjiang, Wang Qiang Designs, Codes and Crytography . 2018,第10期

机译：F_（q〜2）上形式为x〜rh（x〜（q-1））的置换多项式的新构造
4. Orthomorphic Permutation Polynomials of Degree 2~d+1 over Finite Field F_(2~n) [C] . Jiangjiang Guo, Haoran Zheng International Conference on Biomedical Engineering and Informatics . 2009

机译：二〜d + 1过度的正交置换多项式f_（2〜n）
5. A method for constructing groups of permutation polynomials and its application to projective geometry. [D] . Castillo, Chris. 2015

机译：一种构造置换多项式组的方法及其在射影几何中的应用。
6. Limits of zeroes of recursively defined polynomials [O] . S. Beraha, J. Kahane, N. J. Weiss 1975

机译：递归定义的多项式的零极限
7. A Recursive Construction of Permutation Polynomials over $\mathbb{F}_{q^2}$ with Odd Characteristic from R\'{e}dei Functions [O] . Fu, Shihui, Feng, Xiutao, Lin, Dongdai, 2017

机译：上下置换多项式的递推构造来自R \'{e} dei函数的$ \ mathbb {F} _ {q ^ 2} $具有奇数特征
8. Two Conjugate Primitive Recursive Permutations Not Conjugate by a Primitive Recursive Permutation [R] . Finkelstein, M. 1969

机译：两个共轭原始递归排列不是由原始递归排列共轭的

A recursive construction of permutation polynomials over F_(q~2) with odd characteristic related to Redei functions

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