Bounds on Sphere Sizes in the Sum-Rank Metric and Coordinate-Additive Metrics
<|reference_start|>Bounds on Sphere Sizes in the Sum-Rank Metric and Coordinate-Additive Metrics: 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.<|reference_end|>
@article{couvée2024bounds,
    title={Bounds on Sphere Sizes in the Sum-Rank Metric and Coordinate-Additive
  Metrics},
    author={Hugo Sauerbier Couv'ee, Thomas Jerkovits and Jessica Bariffi},
    journal={arXiv preprint arXiv:2404.10666},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.10666},
    primaryClass={cs.IT math.CO math.IT}
}