on the entropy rate of a random walk on t-designs

In this paper, a random walk on  t-designs are considered. we assign a weight to each block and walk randomly on the vertices with a probability proportional to the weight of blocks. this stochastic process is a markov chain. we obtain a stationary distribution for this process and compute its entropy rate. it is seen that, when the blocks have the same weight, the uniform distribution on the vertices is a stationary distribution and the entropy rate depends only on the number of vertices.