环Z_q^n上部分bent函数的谱特征

Spectral Characteristics of PartiallyBentFunctions over Ring Znq

本文在环Ｚｎｑ上讨论了部分ｂｅｎｔ函数的谱特征（ｑ＝ｐ１＊ｐ２，ｐ１，ｐ２是素数），得到了Ｚｎｑ上部分ｂｅｎｔ函数的几个新的刻划，揭示了部分ｂｅｎｔ函数的平衡性、线性结构点及非零谱值点之间的相互关系，并对部分ｂｅｎｔ函数的恒变线性结构点进行了分类，指出了它们之间的相互关系，提出了零因子恒变线性结构点和非零因子恒变线性结构两个新概念。

In this paper,we discuss the Walsh spectral characteristics of partiallybent functions over ring Znq(q=p1*p2,p1、p2 are primes),propose two new concepts—nonzero factor variantpermanently linear structure and zero divisor variant—permanently linear structure,classify the variantpermanently linear structure of partiallybent functions and show their correlation,obtain several new equivalent conditions of partiallybent functions on ring Znq,finally,point out the correlations among balance, linear structure and points taking nonzero spectrum.