Optimal $(r,δ)$-LRCs from monomial-Cartesian codes and their subfield-subcodes
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866917813962145792 |
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| author | Galindo, Carlos Hernando, Fernando Martín-Cruz, Helena |
| author_facet | Galindo, Carlos Hernando, Fernando Martín-Cruz, Helena |
| contents | We study monomial-Cartesian codes (MCCs) which can be regarded as $(r,δ)$-locally recoverable codes (LRCs). These codes come with a natural bound for their minimum distance and we determine those giving rise to $(r,δ)$-optimal LRCs for that distance, which are in fact $(r,δ)$-optimal. A large subfamily of MCCs admits subfield-subcodes with the same parameters of certain optimal MCCs but over smaller supporting fields. This fact allows us to determine infinitely many sets of new $(r,δ)$-optimal LRCs and their parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_01485 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Optimal $(r,δ)$-LRCs from monomial-Cartesian codes and their subfield-subcodes Galindo, Carlos Hernando, Fernando Martín-Cruz, Helena Information Theory We study monomial-Cartesian codes (MCCs) which can be regarded as $(r,δ)$-locally recoverable codes (LRCs). These codes come with a natural bound for their minimum distance and we determine those giving rise to $(r,δ)$-optimal LRCs for that distance, which are in fact $(r,δ)$-optimal. A large subfamily of MCCs admits subfield-subcodes with the same parameters of certain optimal MCCs but over smaller supporting fields. This fact allows us to determine infinitely many sets of new $(r,δ)$-optimal LRCs and their parameters. |
| title | Optimal $(r,δ)$-LRCs from monomial-Cartesian codes and their subfield-subcodes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2205.01485 |