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<p>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 matrices of orders 3 and 4 are used to extend the minimum symbol-pair distance, four new classes of MDS symbol-pair codes and a new class of AMDS symbol-pair codes are derived.</p>

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Several new classes of MDS symbol-pair codes

  • 期刊论文

  • 发表日期：

    2025年9月6日

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  • Xiujing Zheng,
  • Liqi Wang,
  • Shixin Zhu

摘要

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 matrices of orders 3 and 4 are used to extend the minimum symbol-pair distance, four new classes of MDS symbol-pair codes and a new class of AMDS symbol-pair codes are derived.