Repeated-Root Constacyclic Codes with Pair-Metric

Symbol-pair codes are block codes when considering the pair-metric, and are designed to protect against pair-errors occur in the pair-read vector which consisting of overlapping pairs of symbols. A code that achieves the analog of Singleton bound for symbol-pair codes is called a maximum distance separable (MDS) symbol-pair code. The contribution of this letter is twofold. First, we give a lower bound of minimum pair-distance of repeated-root constacyclic codes in terms of minimum Hamming distance, which extends the lower bound given by Chen, Lin and Liu. Second, we give three new classes of MDS symbol-pair codes. As we know, for an MDS symbol-pair code with a fixed minimum pair-distance, the larger the code length of the code has, the higher the code rate is. The first class of MDS symbol-pair codes we show has unbounded code length and the other two classes of MDS symbol-pair codes have larger code lengths than the code lengths of existing MDS symbol-pair codes under the same minimum pair-distance 6.