Generalized Rotation Symmetric and Dihedral Symmetric Boolean Functions - 9 Variable Boolean Functions with Nonlinearity 242
Generalized Rotation Symmetric and Dihedral Symmetric Boolean Functions - 9 Variable Boolean Functions with Nonlinearity 242
复制标题
DOI：
10.1007/978-3-540-77224-8_37
复制
发表时间：
2007-12
期刊：
影响因子：
--
通讯作者：
Selçuk Kavut;M. D. Yücel
中科院分区：
文献类型：
--
作者：
Selçuk Kavut;M. D. Yücel
最近，Kavut，Maitra和Yücel在旋转对称布尔函数（RSBF）类中发现了非线性度为241的9元布尔函数，它严格大于240的弯曲级联界.本文给出了几个非线性度为242的9元布尔函数，它们是通过对RSBF和二面体对称布尔函数（DSBF）类的适当推广而得到的。这些函数在沃尔什谱值中没有任何零点，因此它们不能容易地平衡。该结果还表明一阶Reed-Muller码R（1，9）的覆盖半径至少为242。
Recently, 9-variable Boolean functions having nonlinearity 241, which is strictly greater than the bent concatenation bound of 240, have been discovered in the class of Rotation Symmetric Boolean Functions (RSBFs) by Kavut, Maitra and Yücel. In this paper, we present several 9-variable Boolean functions having nonlinearity of 242, which we obtain by suitably generalizing the classes of RSBFs and Dihedral Symmetric Boolean Functions (DSBFs). These functions do not have any zero in the Walsh spectrum values, hence they cannot be made balanced easily. This result also shows that the covering radius of the first order Reed-Muller codeR(1, 9) is at least 242.