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Bounds on Sphere Sizes in the Sum-Rank Metric and Coordinate-Additive Metrics
April 16, 2024 Β· Declared Dead Β· π Designs, Codes and Cryptography
"No code URL or promise found in abstract"
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Authors
Hugo Beeloo-Sauerbier CouvΓ©e, Thomas Jerkovits, Jessica Bariffi
arXiv ID
2404.10666
Category
cs.IT: Information Theory
Cross-listed
math.CO
Citations
1
Venue
Designs, Codes and Cryptography
Last Checked
4 months ago
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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