标题： 使用循环和常循环码构造最大距离分隔符号对码 显示英文标题

标题： Constructions of Maximum Distance Separable Symbol-Pair Codes Using Cyclic and Constacyclic Codes

摘要： 符号对码是一种新的编码框架，旨在纠正符号对读取信道中的错误。 特别是，最大距离可分（MDS）符号对码是一类具有最佳可能纠错能力的符号对码。 利用循环码和常循环码，我们构造了三类新的MDS符号对码，其最小符号对距离为五或六。 此外，我们发现了一个必要且充分的条件，确保一类循环码成为MDS符号对码。 该条件与一种特殊类型的线性分式变换的某些性质有关。 对这些线性分式变换的详细分析导致了一个算法，该算法生成了许多最小符号对距离为七的MDS符号对码。 显示英文摘要

摘要： Symbol-pair code is a new coding framework which is proposed to correct errors in the symbol-pair read channel. In particular, maximum distance separable (MDS) symbol-pair codes are a kind of symbol-pair codes with the best possible error-correction capability. Employing cyclic and constacyclic codes, we construct three new classes of MDS symbol-pair codes with minimum pair-distance five or six. Moreover, we find a necessary and sufficient condition which ensures a class of cyclic codes to be MDS symbol-pair codes. This condition is related to certain property of a special kind of linear fractional transformations. A detailed analysis on these linear fractional transformations leads to an algorithm, which produces many MDS symbol-pair codes with minimum pair-distance seven.