Piecewise Constructions of Bent and Almost Optimal Boolean Functions

The first aim of this work was to generalize the techniques used in MacWilliams’ and Sloane’s presentation of the Kerdock code and develop a theory of piecewise quadratic Boolean functions. This generalization led us to construct large families of potentially new bent and almost optimal functions from quadratic forms in this piecewise fashion. We show how our motivating example, the Kerdock code, fits into this setting. These constructions were further generalized to non-quadratic bent functions. The resulting constructions design n-variable bent (resp. almost optimal) functions from n-variable bent or almost optimal functions. Communicated by: T. Helleseth     

Some Properties of Bent Functions

First, this paper discusses and sums up some properties of a pair of functions p（x）, q（x） that makes （y ＋ 1）p（x） ＋ yq（x） into a bent function. Then it discusses the properties of bent functions. Also, the upper and lower bounds of the number of bent functions on GF（2）2k are discussed.     

利用有限域上酉几何构作带仲裁的认证码

利用有限域上酉几何构作一类新的带仲裁的认证码,并且计算了所构作认证码的参数以及各种攻击成功的概率.     

利用有限域上奇异伪辛几何构作具有仲裁的认证码

利用有限域上奇异伪辛几何构作了一个新的具有仲裁的认证码,计算了这个码的参数,当发方编码规则和收方解码规则按等概率分布选取时,计算出各种攻击成功的概率.     

m值逻辑函数的谱分解式及广义Bent函数的递归构造

本文用概率方法得到ｍ值逻辑函数Ｃｈｒｅｓｔｅｎｓｏｎ循环谱的分解式,据此考察了ｍ值广义Ｂｅｎｔ函数一些新的性质,给出了递归构造ｍ（ｍ≠２ｍｏｄ４）值广义Ｂｅｎｔ函数的一般方法．     

利用有限域上的向量空间构作一种新的A~2-码

利用有限域上的向量空间的子空间作了一个A~2-码,并计算了该码的参数.在假定发方编码规则和收方解码规则按等概率分布选取时,计算了各种攻击成功的概率.     

An Alternate Characterization of the Bentness of Binary Functions, with Uniqueness

In a previous paper, we have obtained a characterization of the binary bent functions on (GF(2))ⁿ (n even) as linear combinations modulo , with integral coefficients, of characteristic functions (indicators) of -dimensional vector-subspaces of (GF(2))ⁿ. There is no uniqueness of the representation of a given bent function related to this characterization. We obtain now a new characterization for which there is uniqueness of the representation.     

基于有限域上奇异线性空间的码本的新构造

码本广泛应用于码分多址系统用于区分不同用户发出的信号.基于有限域上奇异线性空间构造了一类新的码本.运用奇异线性空间的计数定理,得到了码本的参数,计算了码本的最大互相关振幅,并且给出了最大互相关振幅渐近达到Welch界的条件,证明了所构造的码本是渐近最优码本.