On Poincaré series for codes (Q1126542)

In the model of alphabet coding the author considers several classes of codes (prefix, comma-free, overlapping-free, etc.). The main objects under consideration are the associative algebra \(R\) over a field \(k\) whose ideal of defining relations is generated by the codewords, the homology groups \(H_n(R,k)\), and the Poincaré series \(T(H_n)\) and \(T(R)\). The goal is to express some properties of codes in terms of the Poincaré series. An alternative approach consists in considering the incidence matrices of some graphs corresponding to the code.