2024/04/16 by Hugo Sauerbier Couvée, Couvée, Hugo Beeloo-Sauerbier, Thomas Jerkovits +3 · 1 citation
Computer Science · Engineering · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2404.10666
openalex publication_date 2024/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.