On the zeros of reciprocal Littlewood polynomials

Let $P(z)=\sum_{n=0}^Na_nz^n$ be a Littlewood polynomial of degree $N$, meaning that $a_n\in \{-1, 1\}$. We say that $P$ is reciprocal if $P(z)=z^NP(1/z)$. Borwein, Erdélyi and Littmann (2008) posed the question of determining the minimum number $Z_{\math