A class of functions with low-valued Walsh spectrum

10/26/2019

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by   Fengwei Li, et al.

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Let l≡ 3 4, l 3, be a prime, N=l^2, f=l(l-1)/2 the multiplicative order of a prime p modulo N, and q=p^f. In this paper, we investigate the Walsh spectrum of the monomial functions f(x)= Tr_q/p(x^q-1/l^2) in index two case. In special, we explicitly present the value distribution of the Walsh transform of f(x) if 1+l=4p^h, where h is a class number of Q(√(-l)).