Let $r_i, i=1, \ldots, n$ be Rademacher random variables, i.e. taking values $\pm1$ with probability $\frac 12$ and such that deference of them is equal to $ D$. Let $x_i, i=1, \ldots, n$ be real numbers.
Let $\pi$ be a permutation of the index-set $\{1, \ldots, n\}$ Consider $S=\sum_{i=1}^kr_ix_{\pi(i)}, k<n$.
How to find a moment generating function for $S$?