Bounds on Sphere Sizes in the Sum-Rank Metric and Coordinate-Additive Metrics
arXiv:2404.10666 · doi:10.1007/s10623-025-01604-0
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.