Generating functions of circular codes

We describe in terms of different parameters the generating series of the star of a circular code. We extend the characterization of length distributions of circular codes established for a finite alphabet by Schutzenberger to an arbitrary "weighted" alphabet. In this framework, we give a new characterization of these length distributions. This one directly concerns the coefficients of the generating series of the code instead of the number of primitive conjugacy classes. This result shows that we can decide whether a finite sequence is the length distribution of a circular code. We also establish a necessary and sufficient condition for a series to be the length distribution of a maximal circular code over a finite alphabet. (C) 1999 Academic Press.