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Multiple characters transforms and generalized Boolean functions

机译:多字符转换和广义布尔函数

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摘要

In this paper we investigate generalized Boolean functions whose spectrum is flat with respect to a set of Walsh-Hadamard transforms defined using various complex primitive roots of 1. We also study some differential properties of the generalized Boolean functions in even dimension defined in terms of these different characters. We show that those functions have similar properties to the vectorial bent functions. We next clarify the case of gbent functions in odd dimension. As a by-product of our proofs, more generally, we also provide several results about plateaued functions. Furthermore, we find characterizations of plateaued functions with respect to different characters in terms of second derivatives and fourth moments.
机译:在本文中,我们研究了广义布尔函数,该布尔函数的频谱对于使用1的各种复本元根定义的一组Walsh-Hadamard变换而言是平坦的。不同的字符。我们证明了这些函数与矢量折弯函数具有相似的特性。接下来,我们澄清奇数维中gbent函数的情况。作为我们的证明的副产品,更一般而言,我们还提供了有关平稳功能的一些结果。此外,我们根据二阶导数和四阶矩发现了针对不同特征的平稳函数的表征。

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