Value Distributions of Exponential Sums From Perfect Nonlinear Functions and Their Applications
Value Distributions of Exponential Sums From Perfect Nonlinear Functions and Their Applications
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DOI：
10.1109/tit.2007.903153
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发表时间：
2007-09
影响因子：
2.5
通讯作者：
K. Feng;Jinquan Luo
中科院分区：
文献类型：
--
作者：
K. Feng;Jinquan Luo
在本文中，我们提出了一种统一的方法来确定指数和的多数性sigmaxisinf（q）zetap zetap tr（af（af（x）+bx）（a，bisinfq，q = pm，pges3）这是dembowski-Ostrom多项式或p = 3，f = x（3（k）+1）/2，其中k是奇数，并且（k，m）= 1。作为应用程序，我们确定（1）m序列的相关分布{alambda = tr（gammalambda）}（lambda = 0,1，...）和序列{blambda = tr（f（gammalambda））}（ lambda = 0,1，...）在fp上，其中伽玛是FQ的原始元素，（2）线性代码的重量分布FP由f定义。
In this paper we present a unified way to determine the values and their multiplicities of the exponential sums SigmaxisinF(q)zetap Tr(af(x)+bx)(a,bisinFq,q=pm,pges3) for all perfect nonlinear functions f which is a Dembowski-Ostrom polynomial or p = 3,f=x(3(k)+1)/2 where k is odd and (k,m)=1. As applications, we determine (1) the correlation distribution of the m-sequence {alambda=Tr(gammalambda)}(lambda=0,1,...) and the sequence {blambda=Tr(f(gammalambda))}(lambda=0,1,...) over Fp where gamma is a primitive element of Fq and (2) the weight distributions of the linear codes over Fp defined by f.