Several new classes of MDS symbol-pair codes derived from matrix-product codes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915495748304896 |
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| author | Zheng, Xiujing Wang, Liqi Zhu, Shixin |
| author_facet | Zheng, Xiujing Wang, Liqi Zhu, Shixin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01619 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Several new classes of MDS symbol-pair codes derived from matrix-product codes Zheng, Xiujing Wang, Liqi Zhu, Shixin Information Theory E.4 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. |
| title | Several new classes of MDS symbol-pair codes derived from matrix-product codes |
| topic | Information Theory E.4 |
| url | https://arxiv.org/abs/2401.01619 |