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arXiv · 2111.12946

A Characterization of MDS Symbol-pair Codes over Two Types of Alphabets

Xilin Tang·Weixian Li·Wei Zhao
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Abstract

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.

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Xilin Tang, Weixian Li, Wei Zhao. 2021-11-25. A Characterization of MDS Symbol-pair Codes over Two Types of Alphabets. https://arxiv.org/abs/2111.12946

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