  The notion of a 1-vertex transfer matrix for multi-dimensional codes is
introduced. It is shown that the capacity of such codes, or the topological
entropy, can be expressed as the limit of the logarithm of spectral radii of
1-vertex transfer matrices. Storage and computations using the 1-vertex
transfer matrix are much smaller than storage and computations needed for the
standard transfer matrix. The method is applied to estimate the first 15 digits
of the entropy of the 2-dimensional (0,1) run length limited channel. In order
to compare the computational cost of the new method with the standard transfer
matrix and have rigorous bounds to compare the estimates with a large scale
computation of eigenvalues for the (0,1) run length limited channel in 2 and 3
dimensions have been carried out. This in turn leads to improvements on the
best previous lower and upper bounds for that channel.
