拟Bent函数的性质和构造

Some Properties and Constructions of Quasi-Bent Functions

本文将基本2-群中拟Bent函数的概念推广到一般的有限Abel群中,统一了目前几乎所有的Bent函数概念,完全刻画了一类拟Bent函数和Bent函数的本质联系,给出了几种拟Bent函数的构造方法,拟Bent函数和相对差集的一种关系以及一种用拟Bent函数构造Bent函数的方法.最后,利用Galois环和组合集,找到一类拟Bent函数.

In this paper, we generalize the concept of quasi-bent function in elementary 2-groups to general finite abelian groups, and our quasi-bent function concept concludes nearly all concepts about bent functions up to now. Several constructions are given, and the deep relationship between bent functions and some kind of quasi-bent functions is found. In addition, we find some connection between relative difference sets and quasi-bent functions, and find a way to construct bent functions from quasi-bent functions. In the end, we present some quasi-bent functions by the usage of Galois ring and Building sets.