  The run vector of a binary sequence reflects the run structure of the
sequence, which is given by the set of all substrings of the run length
encoding. The run vector and the aperiodic autocorrelations of a binary
sequence are strongly related. In this paper, we analyze the run vector of
skew-symmetric binary sequences. Using the derived results we present a new and
different proof that there exists no Barker sequence of odd length n > 13.
Barker sequences are binary sequences whose off-peak aperiodic autocorrelations
are all in magnitude at most 1.
