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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.11341 |
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| _version_ | 1866913214578556928 |
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| author | Berhuy, Grégory |
| author_facet | Berhuy, Grégory |
| contents | In this paper, we investigate the existence of self-dual MRD codes $C\subset L^n$, where $L/F$ is an arbitrary field extension of degree $m\geq n$. We then apply our results to the case of finite fields, and prove that if $m=n$ and $F=\mathbb{F}_q$, a self-dual MRD code exists if and only if $q\equiv n\equiv 3 \ [4].$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11341 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the existence of MRD self-dual codes Berhuy, Grégory Information Theory Primary: 94B05, Secondary: 11E04 In this paper, we investigate the existence of self-dual MRD codes $C\subset L^n$, where $L/F$ is an arbitrary field extension of degree $m\geq n$. We then apply our results to the case of finite fields, and prove that if $m=n$ and $F=\mathbb{F}_q$, a self-dual MRD code exists if and only if $q\equiv n\equiv 3 \ [4].$ |
| title | On the existence of MRD self-dual codes |
| topic | Information Theory Primary: 94B05, Secondary: 11E04 |
| url | https://arxiv.org/abs/2312.11341 |