  We study low-energy dipole excitations in the unstable nucleus $^{68}$Ni with
the beyond-mean-field (BMF) subtracted second random-phase-approximation
(SSRPA) model based on Skyrme interactions. First, strength distributions are
compared with available experimental data and transition densities of some
selected peaks are analyzed. The so-called isospin splitting is also discussed
by studying the isoscalar/isovector character of such excitations.
  We estimate then in an indirect way BMF effects on the symmetry energy of
infinite matter and on its slope starting from the BMF SSRPA low-lying strength
distribution. For this, several linear correlations are used, the first one
being a correlation existing between the contribution (associated with the
low-energy strength) to the total energy-weighted sum rule (EWSR) and the slope
of the symmetry energy. BMF estimates for the slope of the symmetry energy can
be extracted in this way. Correlations between such a slope and the
neutron-skin thickness of $^{68}$Ni and correlations between the neutron-skin
thickness of $^{68}$Ni and the electric dipole polarizability times the
symmetry energy are then used to deduce BMF effects on the symmetry energy.
