The Voronoi Region of the Barnes-Wall Lattice $Λ_{16}$
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916452201660416 |
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| author | Pook-Kolb, Daniel Agrell, Erik Allen, Bruce |
| author_facet | Pook-Kolb, Daniel Agrell, Erik Allen, Bruce |
| contents | We give a detailed description of the Voronoi region of the Barnes-Wall lattice $Λ_{16}$, including its vertices, relevant vectors, and symmetry group. The exact value of its quantizer constant is calculated, which was previously only known approximately. To verify the result, we estimate the same constant numerically and propose a new very simple method to quantify the variance of such estimates, which is far more accurate than the commonly used jackknife estimator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_06092 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Voronoi Region of the Barnes-Wall Lattice $Λ_{16}$ Pook-Kolb, Daniel Agrell, Erik Allen, Bruce Information Theory Metric Geometry 11H06, 11H56, 52B20, 52C07 We give a detailed description of the Voronoi region of the Barnes-Wall lattice $Λ_{16}$, including its vertices, relevant vectors, and symmetry group. The exact value of its quantizer constant is calculated, which was previously only known approximately. To verify the result, we estimate the same constant numerically and propose a new very simple method to quantify the variance of such estimates, which is far more accurate than the commonly used jackknife estimator. |
| title | The Voronoi Region of the Barnes-Wall Lattice $Λ_{16}$ |
| topic | Information Theory Metric Geometry 11H06, 11H56, 52B20, 52C07 |
| url | https://arxiv.org/abs/2301.06092 |