Bounds on the minimum distance of locally recoverable codes
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909058395537408 |
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| author | Kurz, Sascha |
| author_facet | Kurz, Sascha |
| contents | We consider locally recoverable codes (LRCs) and aim to determine the smallest possible length $n=n_q(k,d,r)$ of a linear $[n,k,d]_q$-code with locality $r$. For $k\le 7$ we exactly determine all values of $n_2(k,d,2)$ and for $k\le 6$ we exactly determine all values of $n_2(k,d,1)$. For the ternary field we also state a few numerical results. As a general result we prove that $n_q(k,d,r)$ equals the Griesmer bound if the minimum Hamming distance $d$ is sufficiently large and all other parameters are fixed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00418 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bounds on the minimum distance of locally recoverable codes Kurz, Sascha Combinatorics Discrete Mathematics 94B27, 94B05 We consider locally recoverable codes (LRCs) and aim to determine the smallest possible length $n=n_q(k,d,r)$ of a linear $[n,k,d]_q$-code with locality $r$. For $k\le 7$ we exactly determine all values of $n_2(k,d,2)$ and for $k\le 6$ we exactly determine all values of $n_2(k,d,1)$. For the ternary field we also state a few numerical results. As a general result we prove that $n_q(k,d,r)$ equals the Griesmer bound if the minimum Hamming distance $d$ is sufficiently large and all other parameters are fixed. |
| title | Bounds on the minimum distance of locally recoverable codes |
| topic | Combinatorics Discrete Mathematics 94B27, 94B05 |
| url | https://arxiv.org/abs/2401.00418 |