部分Bent函数的本质结构特征及等价刻划

The Essential Structure Characteristic and Equivalent Definition for Partially-Bent Function

本文给出部分Bent函数定义中存在性参数t(参见引理2、引理3)的具体计算方法,并证明了t的唯一性。进一步揭示了部分Bent函数可退化成两种基本形式:一个Bent函数或者一个Bent函数与一个线性头的模二加和。提出了一个新的Bent部分函数的等价定义。

A concrete computational method for the existent parameter t in the definition of partially-Bent function （to see also lemma 2,1emma3） is presented and the uniqueness of the parameter t is proven in this paper. Further, the fact is pointed out that partially-Bent function may degenerate to two kinds of elemental modes： A Bent function or a Bent function adding with a linear head rood 2 in the paper. A new partially Bent function equivalent definition is also proposed.