  Recently, the weight distributions of the duals of the cyclic codes with two
zeros have been obtained for several cases. In this paper we use the method
developed before 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. The problem of finding the weight distribution is
transformed into a problem of evaluating certain character sums over finite
fields, which turns out to be associated with counting the number of points on
some elliptic curves over finite fields. We also treat the special case that
the characteristic of the finite field is 2.
