一类广义Bent函数的构造  

A Family of Generalized Bent Functions

作　　者：陈新姣[1] 张焕国[1] 

机构地区：[1]武汉大学计算机学院/空天信息安全与可信计算教育部重点实验室,湖北武汉430072

出　　处：《武汉大学学报（理学版）》2012年第6期483-487,共5页Journal of Wuhan University:Natural Science Edition

基　　金：国家自然科学基金资助项目(60970115;60970116;61003267)

摘　　要：作为非线性度达到最优的布尔函数——Bent函数可应用于差集、组合论、序列设计密码学等诸多领域.Kumar等人从码分多址技术(CDMA)中相关性最优的序列设计角度将Bent函数的概念推广到奇特征有限域,提出了广义Bent函数.本文基于循环矩阵秩的计算,研究了基于二次型构造的p-元函数是广义Bent函数的充分必要条件,并给出了一类新的广义Bent函数.Bent functions, a class of Boolean functions with the maximal possible nonlinearity, have applications in the fields of different sets, combinatorial theory, sequence design and cryptography. Motivated by the design of optimally correlated sequences used in code division multiple access （CDMA） communication system,Kumar et al. Generalized the notion of Boolean bent functions to the case of functions over an arbitrary finite field in 1985. The present pa- per firstly studied the ranks of circulant matrices over finite field with odd characteristic, based on which we gave a sufficient and necessary condition for bentness of a class of p-ary functions derived from quadratic forms, among which some new p-ary Bent functions were generated.

关 键 词：BENT函数 广义BENT函数 离散傅里叶变换 循环矩阵 

分 类 号：O152[理学—数学]