In order to correct the pair-errors generated during the transmission of modern high-density data storage that the outputs of the channels consist of overlapping pairs of symbols, a new coding scheme named symbol-pair code is proposed. The error-correcting capability of the symbol-pair code is determined by its minimum symbol-pair distance. For such codes, the larger the minimum symbol-pair distance, the better. It is a challenging task to construct symbol-pair codes with optimal parameters, especially, maximum-distance-separable (MDS) symbol-pair codes. In this paper, the permutation equivalence codes of matrix-product codes with underlying matrixes of orders 3 and 4 are used to extend the minimum symbol-pair distance, and six new classes of MDS symbol-pair codes are derived.

翻译：为纠正现代高密度数据存储传输过程中因信道输出由重叠符号对构成而产生的配对错误，提出了一种名为符号对码的新型编码方案。符号对码的纠错能力由其最小符号对距离决定，该距离越大，编码性能越优。构建具有最优参数的符号对码（尤其是极大距离可分（MDS）符号对码）是一项具有挑战性的任务。本文利用以3阶和4阶矩阵为基矩阵的矩阵乘积码的置换等价码扩展最小符号对距离，由此推导出六类新型MDS符号对码。