  The merit factor problem is of practical importance to manifold domains, such
as digital communications engineering, radars, system modulation, system
testing, information theory, physics, chemistry. However, the merit factor
problem is referenced as one of the most difficult optimization problems and it
was further conjectured that stochastic search procedures will not yield merit
factors higher than 5 for long binary sequences (sequences with lengths greater
than 200). Some useful mathematical properties related to the flip operation of
the skew-symmetric binary sequences are presented in this work. By exploiting
those properties, the memory complexity of state-of-the-art stochastic merit
factor optimization algorithms could be reduced from $O(n^2)$ to $O(n)$. As a
proof of concept, a lightweight stochastic algorithm was constructed, which can
optimize pseudo-randomly generated skew-symmetric binary sequences with long
lengths (up to ${10}^5+1$) to skew-symmetric binary sequences with a merit
factor greater than 5. An approximation of the required time is also provided.
The numerical experiments suggest that the algorithm is universal and could be
applied to skew-symmetric binary sequences with arbitrary lengths.
