A new construction of rotation symmetric bent functions with maximal algebraic degree

Sihong Su

doi:10.3934/amc.2019017

Article Contents

2019, Volume 13, Issue 2: 253-265. Doi: 10.3934/amc.2019017

This issue Previous Article Type-preserving matrices and security of block ciphers Next Article Some classes of LCD codes and self-orthogonal codes over finite fields

A new construction of rotation symmetric bent functions with maximal algebraic degree

Sihong Su^,

School of Mathematics and Statistics, Henan University, Kaifeng 475004, China

^* Corresponding author: Sihong Su (E-mail: sush@henu.edu.cn)
^* Corresponding author: Sihong Su (E-mail: sush@henu.edu.cn)

Received: February 28, 2018

Published: January 2019

The author is supported by the National Natural Science Foundation of China (Grant No. 61502147) and the Excellent Youth Program of Henan University (Grant No. yqpy20170063)

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Abstract

In this paper, for any even integer $ n = 2m\ge4 $, a new construction of $ n $-variable rotation symmetric bent function with maximal algebraic degree $ m $ is given as

$ f(x_0,x_1\cdots,x_{n-1}) = \bigoplus\limits_{i = 0}^{m-1}(x_ix_{m+i})\oplus \bigoplus\limits_{i = 0}^{n-1}(x_ix_{i+1}\cdots x_{i+m-2} \overline{x_{i+m}} ), $

whose dual function is

$ \widetilde{f}(x_0,x_1\cdots,x_{n-1}) = \bigoplus\limits_{i = 0}^{m-1}(x_ix_{m+i})\oplus \bigoplus\limits_{i = 0}^{n-1}(x_ix_{i+1}\cdots x_{i+m-2} \overline{x_{i+n-2}} ), $

where $ \overline{x_{i}} = x_{i}\oplus 1 $ and the subscript of $ x $ is modulo $ n $.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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