The geometry of covering codes in the sum-rank metric
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917981335846912 |
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| author | Bonini, Matteo Borello, Martino Byrne, Eimear |
| author_facet | Bonini, Matteo Borello, Martino Byrne, Eimear |
| contents | We introduce the concept of a sum-rank saturating system and outline its correspondence to a covering properties of a sum-rank metric code. We consider the problem of determining the shortest sum-rank-$ρ$-saturating systems of a fixed dimension, which is equivalent to the covering problem in the sum-rank metric. We obtain upper and lower bounds on this quantity. We also give constructions of saturating systems arising from geometrical structures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_12393 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The geometry of covering codes in the sum-rank metric Bonini, Matteo Borello, Martino Byrne, Eimear Combinatorics Information Theory 05B40, 11T71, 51E20, 52C17, 94B75 We introduce the concept of a sum-rank saturating system and outline its correspondence to a covering properties of a sum-rank metric code. We consider the problem of determining the shortest sum-rank-$ρ$-saturating systems of a fixed dimension, which is equivalent to the covering problem in the sum-rank metric. We obtain upper and lower bounds on this quantity. We also give constructions of saturating systems arising from geometrical structures. |
| title | The geometry of covering codes in the sum-rank metric |
| topic | Combinatorics Information Theory 05B40, 11T71, 51E20, 52C17, 94B75 |
| url | https://arxiv.org/abs/2410.12393 |