The weight distributions of a class of cyclic codes III

Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases in Ma et al. (2011) [10], , Ding et al. (2011) [6], , Wang et al. (2012) [15], Xiong (2012) [16,17]. In this paper we solve one more special case. The problem of finding the weight distribution is transformed into a problem of evaluating certain character sums over finite fields, which in turn can be solved by using the Jacobi sums directly.