Symbol-pair codes are block codes with symbol-pair metrics designed to protect against pair-errors that may occur in high-density data storage systems. MDS symbol-pair codes are optimal in the sense that it can attain the highest pair-error correctability within the same code length and code size. Constructing MDS symbol-pair codes is one of the main topics in symbol-pair codes. In this paper, we characterize the symbol-pair distances of some constacyclic codes of arbitrary lengths over finite fields and a class of finite chain rings. Using the characterization of symbol-pair distance, we present several classes of MDS symbol-pair constacyclic codes and show that there is no other MDS symbol-pair code among the class of constacyclic codes except for what we present. Moreover, some of these MDS symbol-pair constacyclic codes over the finite chain rings cannot be obtained by previous work.
翻译:符号-标志代码是带有符号-标志度量的区块代码,目的是保护在高密度数据储存系统中可能发生的双环代码。 MDS 符号-标志代码是最佳的,因为它可以在相同的代码长度和代码大小范围内达到最高的对式传感器。 构建MDS 符号-标志代码是符号-标志代码的主要专题之一。 在本文中,我们描述一些任意长于有限字段和一系列有限链环的集成代码的符号-标志距离。 我们使用符号-标志距离的定性,提出了几种MDS 符号-标志共环代码的类别,并表明除了我们所展示的代码外,在同级代码中没有其他的MDS 符号-标志-标志代码。 此外,这些MDS 符号-标志-标志-圆环对有限链环的一些代码无法通过先前的工作获得。
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