  The high-density data storage technology aims to design high-capacity storage
at a relatively low cost. In order to achieve this goal, symbol-pair codes were
proposed by Cassuto and Blaum \cite{CB10,CB11} to handle channels that output
pairs of overlapping symbols. Such a channel is called symbol-pair read
channel, which introduce new concept called symbol-pair weight and minimum
symbol-pair distance. In this paper, we consider the parameters of two classes
of reducible cyclic codes under the symbol-pair metric. Based on the theory of
cyclotomic numbers and Gaussian period over finite fields, we show the possible
symbol-pair weights of these codes. Their minimum symbol-pair distances are
twice the minimum Hamming distances under some conditions. Moreover, we obtain
some three symbol-pair weight codes and determine their symbol-pair weight
distribution. A class of MDS symbol-pair codes is also established. Among other
results, we determine the values of some generalized cyclotomic numbers.
