Bounds on Sphere Sizes in the Sum-Rank Metric and Coordinate-Additive Metrics
Information Theory
2025-07-04 v3 Combinatorics
math.IT
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.
Cite
@article{arxiv.2404.10666,
title = {Bounds on Sphere Sizes in the Sum-Rank Metric and Coordinate-Additive Metrics},
author = {Hugo Beeloo-Sauerbier Couvée and Thomas Jerkovits and Jessica Bariffi},
journal= {arXiv preprint arXiv:2404.10666},
year = {2025}
}