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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.10666 |
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| _version_ | 1866918080351830016 |
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| author | Couvée, Hugo Beeloo-Sauerbier Jerkovits, Thomas Bariffi, Jessica |
| author_facet | Couvée, Hugo Beeloo-Sauerbier Jerkovits, Thomas Bariffi, Jessica |
| contents | This paper provides new bounds on the size of spheres in any coordinate-additive metric with a particular focus on improving existing bounds in the sum-rank metric. We derive improved upper and lower bounds based on the entropy of a distribution related to the Boltzmann distribution, which work for any coordinate-additive metric. Additionally, we derive new closed-form upper and lower bounds specifically for the sum-rank metric that outperform existing closed-form bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10666 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bounds on Sphere Sizes in the Sum-Rank Metric and Coordinate-Additive Metrics Couvée, Hugo Beeloo-Sauerbier Jerkovits, Thomas Bariffi, Jessica Information Theory Combinatorics This paper provides new bounds on the size of spheres in any coordinate-additive metric with a particular focus on improving existing bounds in the sum-rank metric. We derive improved upper and lower bounds based on the entropy of a distribution related to the Boltzmann distribution, which work for any coordinate-additive metric. Additionally, we derive new closed-form upper and lower bounds specifically for the sum-rank metric that outperform existing closed-form bounds. |
| title | Bounds on Sphere Sizes in the Sum-Rank Metric and Coordinate-Additive Metrics |
| topic | Information Theory Combinatorics |
| url | https://arxiv.org/abs/2404.10666 |