A new family of $2$-scattered subspaces and related MRD codes
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911788054872064 |
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| author | Bartoli, Daniele Ghiandoni, Francesco Giannoni, Alessandro Marino, Giuseppe |
| author_facet | Bartoli, Daniele Ghiandoni, Francesco Giannoni, Alessandro Marino, Giuseppe |
| contents | Scattered subspaces and $h$-scattered subspaces have been extensively studied in recent decades for both theoretical purposes and their connections to various applications. While numerous constructions of scattered subspaces exist, relatively few are known about $h$-scattered subspaces with $h\geq2$. In this paper, we establish the existence of maximum $2$-scattered $\F_q$-subspaces in $V(r,q^6)$ whenever $r\geq 3$, $r\ne 5$, and $q$ is an odd power of $2$. Additionally, we explore the corresponding MRD codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01506 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new family of $2$-scattered subspaces and related MRD codes Bartoli, Daniele Ghiandoni, Francesco Giannoni, Alessandro Marino, Giuseppe Combinatorics Information Theory Scattered subspaces and $h$-scattered subspaces have been extensively studied in recent decades for both theoretical purposes and their connections to various applications. While numerous constructions of scattered subspaces exist, relatively few are known about $h$-scattered subspaces with $h\geq2$. In this paper, we establish the existence of maximum $2$-scattered $\F_q$-subspaces in $V(r,q^6)$ whenever $r\geq 3$, $r\ne 5$, and $q$ is an odd power of $2$. Additionally, we explore the corresponding MRD codes. |
| title | A new family of $2$-scattered subspaces and related MRD codes |
| topic | Combinatorics Information Theory |
| url | https://arxiv.org/abs/2403.01506 |