  A Barker sequence is a binary sequence for which all nontrivial aperiodic
autocorrelations are at most 1 in magnitude. An old conjecture due to Turyn
asserts that there is no Barker sequence of length greater than 13. In 1961,
Turyn and Storer gave an elementary, though somewhat complicated, proof that
this conjecture holds for odd lengths. We give a new and simpler proof of this
result.
