The evaluation of some Ramanujan sums

摘要

Ramanujan sums appear in several contexts in Number Theory and in general their evaluation is not trivial. Recently several authors have used concepts from Number Theory such as exponential sums to provide results in Coding Theory. In this note it is shown that Coding Theory contributes to Number Theory as well. More precisely, it is shown that by means of the homogeneous weight of the codewords of the Simplex code defined over the ring Z/2~(t+1)Z of integers modulo 2~(t+1), the evaluation of some Ramanujan sums is given.