Energy of codes with forbidden distances in 48 dimensions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909423445737472 |
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| author | Boyvalenkov, P. Dragnev, P. |
| author_facet | Boyvalenkov, P. Dragnev, P. |
| contents | We prove the universal optimality of four remarkable spherical 11-designs in 48 dimensions either among all antipodal codes, or all spherical 3-designs, whose inner-products avoid the set $T_1=(-1/3,-1/6) \cup (1/6,1/3)$. We also prove the universal optimality of these configurations among all codes whose distance-avoiding set is $T_2=(-1/2,-1/3) \cup (1/3,1/2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07577 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Energy of codes with forbidden distances in 48 dimensions Boyvalenkov, P. Dragnev, P. Combinatorics Metric Geometry We prove the universal optimality of four remarkable spherical 11-designs in 48 dimensions either among all antipodal codes, or all spherical 3-designs, whose inner-products avoid the set $T_1=(-1/3,-1/6) \cup (1/6,1/3)$. We also prove the universal optimality of these configurations among all codes whose distance-avoiding set is $T_2=(-1/2,-1/3) \cup (1/3,1/2)$. |
| title | Energy of codes with forbidden distances in 48 dimensions |
| topic | Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2412.07577 |