论文标题
新的负面功能
A new class of negabent functions
论文作者
论文摘要
引入了负函数作为弯曲函数的概括，这些功能在编码理论和加密中具有应用。在本文中，我们将否定函数的概念扩展到了从$ \ mathbb {z} _q^n $定义的函数，到$ \ mathbb {z} _ {2q} $（$ 2Q $ -2Q $ -NEGABENT） $ Q $。为此，当前设置中引入了新的统一变换（Nega-Hadamard变换），并讨论了其某些属性。提出了一些与$ 2Q $ -NEGABENT功能有关的结果。我们提供两个$ 2Q $ -NEGABENT功能的构造。在第一个构造中，当$ n $变量上的$ 2Q $ -NEGABENT函数是$ n $变量时的，当$ q $是一个正面的整数时。在第二个结构中，为任意正整数$ q \ ge 2 $构建了两个变量上的$ 2Q $ -NEGABENT函数。还提供了一些$ 2Q $ -NEGABENT函数的示例，用于不同值的$ Q $和$ n $。
Negabent functions were introduced as a generalization of bent functions, which have applications in coding theory and cryptography. In this paper, we have extended the notion of negabent functions to the functions defined from $\mathbb{Z}_q^n$ to $\mathbb{Z}_{2q}$ ($2q$-negabent), where $q \geq 2$ is a positive integer and $\mathbb{Z}_q$ is the ring of integers modulo $q$. For this, a new unitary transform (the nega-Hadamard transform) is introduced in the current set up, and some of its properties are discussed. Some results related to $2q$-negabent functions are presented. We present two constructions of $2q$-negabent functions. In the first construction, $2q$-negabent functions on $n$ variables are constructed when $q$ is an even positive integer. In the second construction, $2q$-negabent functions on two variables are constructed for arbitrary positive integer $q \ge 2$. Some examples of $2q$-negabent functions for different values of $q$ and $n$ are also presented.
