Locally Repairable Convertible Codes: Improved Lower Bound and General Construction
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909975616421888 |
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| author | Ge, Songping Cai, Han Tang, Xiaohu |
| author_facet | Ge, Songping Cai, Han Tang, Xiaohu |
| contents | In this paper, we consider the convertible code with locally repairable property. We present an improved lower bound on access cost associated with $(r,δ)$. Then, we provide a general construction of convertible codes with optimal access cost which shows that those codes can be with super-linear length or maximum repairable property. Additionally, employing the known locally repairable codes with super-linear length or maximum repairable property, we provide explicit constructions of convertible codes with super-linear length or maximum repairable property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06734 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Locally Repairable Convertible Codes: Improved Lower Bound and General Construction Ge, Songping Cai, Han Tang, Xiaohu Information Theory In this paper, we consider the convertible code with locally repairable property. We present an improved lower bound on access cost associated with $(r,δ)$. Then, we provide a general construction of convertible codes with optimal access cost which shows that those codes can be with super-linear length or maximum repairable property. Additionally, employing the known locally repairable codes with super-linear length or maximum repairable property, we provide explicit constructions of convertible codes with super-linear length or maximum repairable property. |
| title | Locally Repairable Convertible Codes: Improved Lower Bound and General Construction |
| topic | Information Theory |
| url | https://arxiv.org/abs/2504.06734 |