A method to find the volume of a sphere in the Lee metric, and its applications

Abstract

We develop general techniques to bound the size of the balls of a given radius r for q-ary discrete metrics, using the generating function for the metric and Sanov’s theorem, that reduces to the known bound in the case of the Hamming metric and gives us a new bound in the case of the Lee metric. We use the techniques developed to find Hamming, Elias-Bassalygo and Gilbert-Varshamov bounds for the Lee metric.