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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2507.00609 |
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| _version_ | 1866914294034071552 |
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| author | Berhuy, G. Molina, J. |
| author_facet | Berhuy, G. Molina, J. |
| contents | We study the rank weight hierarchy of linear codes which are stable under a linear endomorphism defined over the base field, in particular when the endomorphism is cyclic. In this last case, we give a necessary and sufficient condition for such a code to have first rank weight equal to $1$ in terms of its generator polynomial, as well as an explicit formula for its last rank weight. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00609 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the rank weight hierarchy of $M$-codes Berhuy, G. Molina, J. Information Theory We study the rank weight hierarchy of linear codes which are stable under a linear endomorphism defined over the base field, in particular when the endomorphism is cyclic. In this last case, we give a necessary and sufficient condition for such a code to have first rank weight equal to $1$ in terms of its generator polynomial, as well as an explicit formula for its last rank weight. |
| title | On the rank weight hierarchy of $M$-codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2507.00609 |