  The identification of binary sequences with large merit factor (small
mean-squared aperiodic autocorrelation) is an old problem of complex analysis
and combinatorial optimization, with practical importance in digital
communications engineering and condensed matter physics. We establish the
asymptotic merit factor of several families of binary sequences and thereby
prove various conjectures, explain numerical evidence presented by other
authors, and bring together within a single framework results previously
appearing in scattered form. We exhibit, for the first time, families of
skew-symmetric sequences whose asymptotic merit factor is as large as the best
known value (an algebraic number greater than 6.34) for all binary sequences;
this is interesting in light of Golay's conjecture that the subclass of
skew-symmetric sequences has asymptotically optimal merit factor. Our methods
combine Fourier analysis, estimation of character sums, and estimation of the
number of lattice points in polyhedra.
