Generating functions of circular codes

We describe in terms of different parameters the generating series of the s tar of a circular code. We extend the characterization of length distributi ons of circular codes established for a finite alphabet by Schutzenberger t o an arbitrary "weighted" alphabet. In this framework, we give a new charac terization of these length distributions. This one directly concerns the co efficients of the generating series of the code instead of the number of pr imitive conjugacy classes. This result shows that we can decide whether a f inite sequence is the length distribution of a circular code. We also estab lish a necessary and sufficient condition for a series to be the length dis tribution of a maximal circular code over a finite alphabet. (C) 1999 Acade mic Press.