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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1911.07485 |
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| _version_ | 1866913334532505600 |
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| author | Galindo, Carlos Hernando, Fernando Munuera, Carlos |
| author_facet | Galindo, Carlos Hernando, Fernando Munuera, Carlos |
| contents | A locally recoverable (LRC) code is a code over a finite field $\mathbb{F}_q$ such that any erased coordinate of a codeword can be recovered from a small number of other coordinates in that codeword. We construct LRC codes correcting more than one erasure, which are subfield-subcodes of some $J$-affine variety codes. For these LRC codes, we compute localities $(r, δ)$ that determine the minimum size of a set $\bar{R}$ of positions so that any $δ- 1$ erasures in $\bar{R}$ can be recovered from the remaining $r$ coordinates in this set. We also show that some of these LRC codes with lengths $n\gg q$ are $(δ-1)$-optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_07485 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Locally recoverable $J$-affine variety codes Galindo, Carlos Hernando, Fernando Munuera, Carlos Information Theory 94B05 94B20 11T71 A locally recoverable (LRC) code is a code over a finite field $\mathbb{F}_q$ such that any erased coordinate of a codeword can be recovered from a small number of other coordinates in that codeword. We construct LRC codes correcting more than one erasure, which are subfield-subcodes of some $J$-affine variety codes. For these LRC codes, we compute localities $(r, δ)$ that determine the minimum size of a set $\bar{R}$ of positions so that any $δ- 1$ erasures in $\bar{R}$ can be recovered from the remaining $r$ coordinates in this set. We also show that some of these LRC codes with lengths $n\gg q$ are $(δ-1)$-optimal. |
| title | Locally recoverable $J$-affine variety codes |
| topic | Information Theory 94B05 94B20 11T71 |
| url | https://arxiv.org/abs/1911.07485 |