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Value Distributions of Exponential Sums From Perfect Nonlinear Functions and Their Applications

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2 Author(s)
Keqin Feng ; Tsinghua Univ., Beijing ; Jinquan Luo

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.

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Information Theory, IEEE Transactions on  (Volume:53 ,  Issue: 9 )