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arXiv · 2404.10666

Bounds on Sphere Sizes in the Sum-Rank Metric and Coordinate-Additive Metrics

Hugo Beeloo-Sauerbier Couvée·Thomas Jerkovits·Jessica Bariffi
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Abstract

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.

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Hugo Beeloo-Sauerbier Couvée, Thomas Jerkovits, Jessica Bariffi. 2024-04-16. Bounds on Sphere Sizes in the Sum-Rank Metric and Coordinate-Additive Metrics. https://doi.org/10.1007/s10623-025-01604-0

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