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.

翻译：Negabent 函数被引入为对弯曲函数的概括化,这些函数在编码理论和密码学中具有应用。在本文中,我们将负负函数的概念扩展至从$\mathbb ⁇ q ⁇ q ⁇ q}美元(2q$-negabent美元)到美元(2q$-negabent美元)这一定义的函数,其中,$q\geq 2美元是一个正整数,$\mathb ⁇ qq美元是整数的圆环。为此,在目前的设置中引入了一种新的统一变换(nega-Hadamard变换),并讨论了其中的一些属性。介绍了与2q$-negabent函数有关的一些结果。在第一个构造中,当美元为正整数时,则构建了$2q$-negaben变量的函数。在第二个构造中,为2q美元-negab函数的任意正整美元=2美元。还介绍了“美元”和“美元”美元”的不同函数的一些例子。