Some algebraic properties of finite binary sequences

We study properties of differences of fi…nite binary sequences with a fi…xed number of ones. We show that any binary sequence consisting of $m$ terms (except of the sequence $(1, 0, \ldots, 0)$) can be presented as a difference of two sequences having exactly $n$ ones, whenever $\frac{1}{4} m < n < \frac{3}{4}m$.