On codes that avoid specified differences

Certain magnetic recording applications call for a large number of sequences whose differences do not include certain disallowed binary patterns. We show that the number of such sequences increases exponentially with their length and that the growth rate, or capacity, is the logarithm of the joint spectral radius of an appropriately defined set of matrices. We derive a new algorithm for determining the joint spectral radius of sets of nonnegative matrices and combine it with existing algorithms to determine the capacity of several sets of disallowed differences that arise in practice.