Short rank-metric codes and scattered subspaces
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
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| _version_ | 1866914673025089536 |
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| author | Lia, Stefano Longobardi, Giovanni Marino, Giuseppe Trombetti, Rocco |
| author_facet | Lia, Stefano Longobardi, Giovanni Marino, Giuseppe Trombetti, Rocco |
| contents | By exploiting the connection between scattered $\mathbb{F}_q$-subspaces of $\mathbb{F}_{q^m}^3$ and minimal non degenerate $3$-dimensional rank metric codes of $\mathbb{F}_{q^m}^{n}$, $n \geq m+2$, described in [2], we will exhibit a new class of codes with parameters $[m+2,3,m-2]_{q^m/q}$ for infinite values of $q$ and $m \geq 5$ odd. Moreover, by studying the geometric structures of these scattered subspaces, we determine the rank weight distribution of the associated codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_01315 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Short rank-metric codes and scattered subspaces Lia, Stefano Longobardi, Giovanni Marino, Giuseppe Trombetti, Rocco Information Theory Combinatorics By exploiting the connection between scattered $\mathbb{F}_q$-subspaces of $\mathbb{F}_{q^m}^3$ and minimal non degenerate $3$-dimensional rank metric codes of $\mathbb{F}_{q^m}^{n}$, $n \geq m+2$, described in [2], we will exhibit a new class of codes with parameters $[m+2,3,m-2]_{q^m/q}$ for infinite values of $q$ and $m \geq 5$ odd. Moreover, by studying the geometric structures of these scattered subspaces, we determine the rank weight distribution of the associated codes. |
| title | Short rank-metric codes and scattered subspaces |
| topic | Information Theory Combinatorics |
| url | https://arxiv.org/abs/2306.01315 |