  A lattice QCD study of the strong decay width and coupling constant of
decuplet baryons to an octet baryon - pion state is presented. The transfer
matrix method is used to obtain the overlap of lattice states with decuplet
baryon quantum numbers on the one hand and octet baryon-pion quantum numbers on
the other as an approximation to the matrix element of the corresponding
transition. By making use of leading order effective field theory, the coupling
constants, as well as the widths for the various decay channels are determined.
The transitions studied are $ \Delta \to \pi \,N$, $\Sigma^* \to \Lambda\,\pi$,
$\Sigma^* \to \Sigma\,\pi$ and $\Xi^* \to \Xi\,\pi$. We obtain results for two
ensembles of $N_f=2+1$ dynamical fermion configurations, one using domain wall
valence quarks on a staggered sea at a pion mass of $350\,\mathrm{MeV}$ and a
box size of $3.4\,\mathrm{fm}$ and a second one using domain wall sea and
valence quarks at pion mass $180\,\mathrm{MeV}$ and box size
$4.5\,\mathrm{fm}$.
