About the generalized Hamming weights of matrix-product codes
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909536932069376 |
|---|---|
| author | San-José, Rodrigo |
| author_facet | San-José, Rodrigo |
| contents | We derive a general lower bound for the generalized Hamming weights of nested matrix-product codes, with a particular emphasis on the cases with two and three constituent codes. We also provide an upper bound which is reminiscent of the bounds used for the minimum distance of matrix-product codes. When the constituent codes are two Reed-Solomon codes, we obtain an explicit formula for the generalized Hamming weights of the resulting matrix-product code. We also deal with the non-nested case for the case of two constituent codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11810 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | About the generalized Hamming weights of matrix-product codes San-José, Rodrigo Information Theory 94B05 (Primary) 94B65, 11T71 (Secondary) We derive a general lower bound for the generalized Hamming weights of nested matrix-product codes, with a particular emphasis on the cases with two and three constituent codes. We also provide an upper bound which is reminiscent of the bounds used for the minimum distance of matrix-product codes. When the constituent codes are two Reed-Solomon codes, we obtain an explicit formula for the generalized Hamming weights of the resulting matrix-product code. We also deal with the non-nested case for the case of two constituent codes. |
| title | About the generalized Hamming weights of matrix-product codes |
| topic | Information Theory 94B05 (Primary) 94B65, 11T71 (Secondary) |
| url | https://arxiv.org/abs/2407.11810 |