Coding Closed Geodesics on Modular Surfaces by Use of the Elias Type of Codes

| In this paper we show a procedure for coding geodesics on modular surfaces by use of the Elias type of code for source coding. This procedure implies that the arithmetic codes associated with each primitive hyperbolic matrix can be viewed as a generalization of the Elias codes. The main result of this paper establishes the procedures to be followed in order to identify the arithmetic code and the axis of the geodesic when only the probability associated with the geodesic is given. Several examples are also considered.