On the distribution of auto-correlation value of balanced Boolean functions
Yu Zhou · Advances in Mathematics of Communications · 2013
In this paper, we study the lower bound on the sum-of-square indicator of balanced Boolean functions obtained by Son, et al. in 1998, and give a sufficient and necessary condition under which balanced Boolean functions achieve this lower bound. We introduce a new general class of balanced Boolean functions in $n$ variables $(n\geq 4)$ with optimal auto-correlation distribution, and we study two sub-classes more explicitely. Finally, we study the sets of Boolean functions having a same auto-correlation distribution, and derive a lower bound on the number of elements in such set.