The Shannon capacity of M-ary constrained codes

We consider a class of constrained codes that prohibits the occurrence of substrings from a finite set F of sequences of finite length over an alphabet Z_A=(0,1,...,A-1). The set F is called the set of distinguished substrings. The capacity of the code S, denoted as C, was defined by Shannon as C=lim_n→∞log₂ c_n/n. The standard method of evaluating the capacity is to take log₂λ, where λ is the largest real eigenvalue of the adjacent matrix that reflects the constraint. The purpose of this paper is to present a systematic method, based on combinatorial enumeration techniques, to find the number of sequences of length n in S,c_n satisfying a specified constraint. The capacity is expressed as the base two logarithm of the inverse of the largest real root of the denominator polynomial in the generating series which enumerates the sequences