  Usually, it is difficult to determine the weight distribution of an
irreducible cyclic code. In this paper, we discuss the case when an irreducible
cyclic code has the maximal number of distinct nonzero weights and give a
necessary and sufficient condition. In this case, we also obtain a divisible
property for the weight of a codeword. Further, we present a necessary and
sufficient condition for an irreducible cyclic code with only one nonzero
weight. Finally, we determine the weight distribution of an irreducible cyclic
code for some cases.
