Griesmer Bound and Constructions of Linear Codes in $b$-Symbol Metric
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913191376715776 |
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| author | Luo, Gaojun Ezerman, Martianus Frederic Güneri, Cem Ling, San Özbudak, Ferruh |
| author_facet | Luo, Gaojun Ezerman, Martianus Frederic Güneri, Cem Ling, San Özbudak, Ferruh |
| contents | The $b$-symbol metric is a generalization of the Hamming metric. Linear codes, in the $b$-symbol metric, have been used in the read channel whose outputs consist of $b$ consecutive symbols. The Griesmer bound outperforms the Singleton bound for $\mathbb{F}_q$-linear codes in the Hamming metric, when $q$ is fixed and the length is large enough. This scenario is also applicable in the $b$-symbol metric. Shi, Zhu, and Helleseth recently made a conjecture on cyclic codes in the $b$-symbol metric. In this paper, we present the $b$-symbol Griesmer bound for linear codes by concatenating linear codes and simplex codes. Based on cyclic codes and extended cyclic codes, we propose two families of distance-optimal linear codes with respect to the $b$-symbol Griesmer bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04941 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Griesmer Bound and Constructions of Linear Codes in $b$-Symbol Metric Luo, Gaojun Ezerman, Martianus Frederic Güneri, Cem Ling, San Özbudak, Ferruh Information Theory The $b$-symbol metric is a generalization of the Hamming metric. Linear codes, in the $b$-symbol metric, have been used in the read channel whose outputs consist of $b$ consecutive symbols. The Griesmer bound outperforms the Singleton bound for $\mathbb{F}_q$-linear codes in the Hamming metric, when $q$ is fixed and the length is large enough. This scenario is also applicable in the $b$-symbol metric. Shi, Zhu, and Helleseth recently made a conjecture on cyclic codes in the $b$-symbol metric. In this paper, we present the $b$-symbol Griesmer bound for linear codes by concatenating linear codes and simplex codes. Based on cyclic codes and extended cyclic codes, we propose two families of distance-optimal linear codes with respect to the $b$-symbol Griesmer bound. |
| title | Griesmer Bound and Constructions of Linear Codes in $b$-Symbol Metric |
| topic | Information Theory |
| url | https://arxiv.org/abs/2401.04941 |