  We consider a generalized coagulation-decoagulation system on a
one-dimensional discrete lattice with reflecting boundaries. It is known that a
Bernoulli shock measure with two shock fronts might have a simple random-walk
dynamics, provided that some constraints on the microscopic reaction rates of
this system are fulfilled. Under these constraints the steady-state of the
system can be written as a linear superposition of such shock measures. We show
that the coefficients of this expansion can be calculated using the
finite-dimensional representation of the quadratic algebra of the system
obtained from a matrix-product approach.
