  Recently, there has been intensive research on the weight distributions of
cyclic codes. In this paper, we compute the weight distributions of three
classes of cyclic codes with Niho exponents. More specifically, we obtain two
classes of binary three-weight and four-weight cyclic codes and a class of
nonbinary four-weight cyclic codes. The weight distributions follow from the
determination of value distributions of certain exponential sums. Several
examples are presented to show that some of our codes are optimal and some have
the best known parameters.
