On the coordinates of minimal vectors in a Minkowski-reduced basis
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866916429699219456 |
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| author | Horváth, Ákos G. |
| author_facet | Horváth, Ákos G. |
| contents | Finding the shortest vectors in a lattice is an NP-hard problem, so low-dimensional results also play an essential role in lattice reduction theory. Using Ryskov's result for the admissible centerings and Tammela's result for determining the Minkowski-reduced form, we prove that the absolute values of the coordinates of a minimal vector on a six-dimensional Minkowski-reduced basis are less than or equal to three. To sharpen P. Tammela's work, we combine some lattice geometry arguments with the aforementioned theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_05154 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the coordinates of minimal vectors in a Minkowski-reduced basis Horváth, Ákos G. Metric Geometry 11H50, 11H55 Finding the shortest vectors in a lattice is an NP-hard problem, so low-dimensional results also play an essential role in lattice reduction theory. Using Ryskov's result for the admissible centerings and Tammela's result for determining the Minkowski-reduced form, we prove that the absolute values of the coordinates of a minimal vector on a six-dimensional Minkowski-reduced basis are less than or equal to three. To sharpen P. Tammela's work, we combine some lattice geometry arguments with the aforementioned theoretical results. |
| title | On the coordinates of minimal vectors in a Minkowski-reduced basis |
| topic | Metric Geometry 11H50, 11H55 |
| url | https://arxiv.org/abs/2102.05154 |