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 $4.5,mathrm{fm}$.
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