A class of functions with low-valued Walsh spectrum

Abstract

Let $l\equiv 3(\mathrm{mod}4)$, $l\ne 3$, be a prime, $N=l^2$, $f=\frac{l(l-1)}{2}$ 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 $f(x)={\mathrm{Tr}}_{q/p}(x^{\frac{q-1}{l^2}})$ 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 $\mathbb{Q}(\sqrt{-l})$.

15 pages. To appear in Discrete Applied Mathematics

References in corpus (1)

• Complete Solving for Explicit Evaluation of Gauss Sums in the Index 2 Case