A property of finite maximal codes (Q1373093)

The author gives a characterization of finite maximal codes and uses this to find classes of codes with no finite completions. The author proves that for a finite maximal code, \(C\), over a two-letter alphabet, \(\{a,b\}\) where \(a^n,b^m\in C\), there is a corresponding \(m\)-multifactorization of \(\mathbb{Z}_n\). This result is then used to construct examples of codes that have no finite completion.