  We study the static and dynamical properties of a long-range Kitaev chain,
i.e., a $p$-wave superconducting chain in which the superconducting pairing
decays algebraically as $1/l^{\alpha}$, where $l$ is the distance between the
two sites and $\alpha$ is a positive constant. Considering very large system
sizes, we show that when $\alpha >1$, the system is topologically equivalent to
the short-range Kitaev chain with massless Majorana modes at the ends of the
system; on the contrary, for $\alpha <1$, there exist symmetry protected
massive Dirac end modes. We further study the dynamical phase boundary of the
model when periodic $\delta$-function kicks are applied to the chemical
potential; we specially focus on the case $\alpha >1$ and analyze the
corresponding Floquet quasienergies. Interestingly, we find that new
topologically protected massless end modes are generated at the quasienergy
$\pi/T$ (where $T$ is the time period of driving) in addition to the end modes
at zero energies which exist in the static case. By varying the frequency of
kicking, we can produce topological phase transitions between different
dynamical phases. Finally, we propose some bulk topological invariants which
correctly predict the number of massless end modes at quasienergies equal to 0
and $\pi/T$ for a periodically kicked system with $\alpha > 1$.
