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.

翻译：高密度数据存储技术旨在以相对较低的成本设计高容量存储。为实现这一目标，Cassuto和Blaum \cite{CB10,CB11}提出了符号对编码，用于处理输出重叠符号对的信道。这种信道被称为符号对读取信道，其引入了称为符号对权重和最小符号对距离的新概念。本文考虑了两类可约循环码在符号对度量下的参数。基于有限域上的分圆数与高斯周期理论，我们展示了这些码可能的符号对权重。在某些条件下，它们的最小符号对距离是汉明最小距离的两倍。此外，我们得到了一些三符号对权重码，并确定了其符号对权重分布。同时建立了一类MDS符号对码。在其他结果中，我们确定了一些广义分圆数的取值。