广义bent函数的性质与构造  

Nature and Structure of Generalized Bent Functions

作　　者：梅瑞[1] 

机构地区：[1]四川大学,四川成都610065

出　　处：《成都航空职业技术学院学报》2013年第3期24-26,共3页Journal of Chengdu Aeronautic Polytechnic

摘　　要：广义bent函数f(x)对应的每个Walsh谱取值均相等,此时f(x)与仿射函数g(x)=x×y+b(y∈iimq,b∈Zq)的距离可证明都相等,这使得广义bent函数的非线性度达到最大。这种函数在保密和通信中有许多重要的应用。本文首先讨论了广义bent函数的一些性质,且通过这些性质在已有结论的基础上给出构造广义bent函数的一些方法,并在之后给出了证明。Bent function is a special class of boolean functions, generalized bent function is the promotion of bent functions. Each Walsh function value due to generalized bent function are equal, then the f（x） with all the affine function g（x）=x×y＋b（y∈ii,b∈Zq）distance equal to this function in confidentiality and communication in many heavy. To ap-plications what q ≥ 2 and m ≥1 exists Zq on generalized bent functions, basic questions about the generalized bent func- tions to do all and, if present test configuration （or as many as possible） generalized bent functions, and these functions are classified. Gives a structure to do has been concluded on the basis of generalized bent function method, which can help us to quickly constructed of bent functions, and then prove.

关 键 词：有限域 WALSH变换 BENT函数 广义BENT函数 

分 类 号：G416[文化科学—教育学]