On spherical codes with inner products in a prescribed interval
| Autor: | Boyvalenkov, P. G., Dragnev, P. D., Hardin, D. P., Saff, E. B., Stoyanova, M. M. |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We develop a framework for obtaining linear programming bounds for spherical codes whose inner products belong to a prescribed subinterval $[\ell,s]$ of $[-1,1)$. An intricate relationship between Levenshtein-type upper bounds on cardinality of codes with inner products in $[\ell,s]$ and lower bounds on the potential energy (for absolutely monotone interactions) for codes with inner products in $[\ell,1)$ (when the cardinality of the code is kept fixed) is revealed and explained. Thereby, we obtain a new extension of Levenshtein bounds for such codes. The universality of our bounds is exhibited by a unified derivation and their validity for a wide range of codes and potential functions. Comment: 18 pages, 1 figure |
| Databáze: | arXiv |
| Externí odkaz: |
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