关于F_q上的k阶拟广义Bent函数

On k-Order Quasi-Generalized-Bent Function Over F_q

文章给出了一般有限域上k阶拟广义Bent函数的定义,研究了它的一些基本性质,并考虑了它和素域上向量函数的关系。证明了k阶拟广义Bent函数的一个判别条件,同时给出了有限域上n元k阶拟广义Bent函数的典型构造。结果表明对于一般有限域上k阶拟广义Bent函数的研究可以转化为素域上对应的向量函数的研究,从而为有限域上k阶拟广义Bent函数的存在性、构造等问题提供了新的思路和方法。

In this paper, the definition of k-order quasi-generalized-Bent function over finite fields is proposed, the properties are discussed, and the relationship between k-order quasi-generalized-Bent function over finite fields and the vector functions over prime fields is studied. The sufficient and necessary condition of the k-order quasi-generalized-Bent function is proved. It gets a typical construction over finite fields. By the proposed definition, it is shown that the k-order quasi-generalized- Bent function over finite fields can be studied by vector functions over prime fields. Furthermore, we can discuss it in the new way.