  Recently, the weight distributions of the duals of the cyclic codes with two
zeros have been obtained for several cases. In this paper we provide a slightly
different approach toward the general problem and use it to solve one more
special case. We make extensive use of standard tools in number theory such as
characters of finite fields, the Gauss sums and the Jacobi sums to transform
the problem of finding the weight distribution into a problem of evaluating
certain character sums over finite fields, which on the special case is related
with counting the number of points on some elliptic curves over finite fields.
Other cases are also possible by this method.
