Functional Delsarte-Goethals-Seidel-Kabatianskii-Levenshtein-Pfender Bound
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916844879740928 |
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| author | Krishna, K. Mahesh |
| author_facet | Krishna, K. Mahesh |
| contents | Pfender \textit{[J. Combin. Theory Ser. A, 2007]} provided a one-line proof for a variant of the Delsarte-Goethals-Seidel-Kabatianskii-Levenshtein upper bound for spherical codes, which offers an upper bound for the celebrated (Newton-Gregory) kissing number problem. Motivated by this proof, we introduce the notion of codes in pointed metric spaces (in particular on Banach spaces) and derive a nonlinear (functional) Delsarte-Goethals-Seidel-Kabatianskii-Levenshtein-Pfender upper bound for spherical codes. We also introduce nonlinear (functional) Kissing Number Problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_05047 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Functional Delsarte-Goethals-Seidel-Kabatianskii-Levenshtein-Pfender Bound Krishna, K. Mahesh Functional Analysis Combinatorics Optimization and Control 94B65, 54E35 Pfender \textit{[J. Combin. Theory Ser. A, 2007]} provided a one-line proof for a variant of the Delsarte-Goethals-Seidel-Kabatianskii-Levenshtein upper bound for spherical codes, which offers an upper bound for the celebrated (Newton-Gregory) kissing number problem. Motivated by this proof, we introduce the notion of codes in pointed metric spaces (in particular on Banach spaces) and derive a nonlinear (functional) Delsarte-Goethals-Seidel-Kabatianskii-Levenshtein-Pfender upper bound for spherical codes. We also introduce nonlinear (functional) Kissing Number Problem. |
| title | Functional Delsarte-Goethals-Seidel-Kabatianskii-Levenshtein-Pfender Bound |
| topic | Functional Analysis Combinatorics Optimization and Control 94B65, 54E35 |
| url | https://arxiv.org/abs/2411.05047 |