Linear codes for $b$-symbol read channels attaining the Griesmer bound
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913936271474688 |
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| author | Kurz, Sascha |
| author_facet | Kurz, Sascha |
| contents | Reading channels where $b$-tuples of adjacent symbols are read at every step have e.g.\ applications in storage. Corresponding bounds and constructions of codes for the $b$-symbol metric, especially the pair-symbol metric where $b=2$, were intensively studied in the last fifteen years. Here we determine the optimal code parameters of linear codes in the $b$-symbol metric assuming that the minimum distance is sufficiently large. We also determine the optimal parameters of linear binary codes in the pair-symbol metric for small dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07728 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear codes for $b$-symbol read channels attaining the Griesmer bound Kurz, Sascha Information Theory Combinatorics 05B25, 94B65, 94B60 Reading channels where $b$-tuples of adjacent symbols are read at every step have e.g.\ applications in storage. Corresponding bounds and constructions of codes for the $b$-symbol metric, especially the pair-symbol metric where $b=2$, were intensively studied in the last fifteen years. Here we determine the optimal code parameters of linear codes in the $b$-symbol metric assuming that the minimum distance is sufficiently large. We also determine the optimal parameters of linear binary codes in the pair-symbol metric for small dimensions. |
| title | Linear codes for $b$-symbol read channels attaining the Griesmer bound |
| topic | Information Theory Combinatorics 05B25, 94B65, 94B60 |
| url | https://arxiv.org/abs/2507.07728 |