  We study a discrete-time branching annihilating random walk (BARW) on the
$d$-dimensional lattice. Each particle produces a Poissonian number of
offspring with mean $\mu$ which independently move to a uniformly chosen site
within a fixed distance $R$ from their parent's position. Whenever a site is
occupied by at least two particles, all the particles at that site are
annihilated. We prove that for any $\mu>1$ the process survives when $R$ is
sufficiently large. For fixed $R$ we show that the process dies out if $\mu$ is
too small or too large. Furthermore, we exhibit an interval of $\mu$-values for
which the process survives and possesses a unique non-trivial ergodic
equilibrium for $R$ sufficiently large. We also prove complete convergence for
that case.
