Whitney Numbers of Rank-Metric Lattices and Code Enumeration
Combinatorics
2024-12-19 v1 Information Theory
math.IT
Abstract
We investigate the Whitney numbers of the first kind of rank-metric lattices, which are closely linked to the open problem of enumerating rank-metric codes having prescribed parameters. We apply methods from the theory of hyperovals and linear sets to compute these Whitney numbers for infinite families of rank-metric lattices. As an application of our results, we prove asymptotic estimates on the density function of certain rank-metric codes that have been conjectured in previous work.
Keywords
Cite
@article{arxiv.2412.13906,
title = {Whitney Numbers of Rank-Metric Lattices and Code Enumeration},
author = {Giuseppe Cotardo and Alberto Ravagnani and Ferdinando Zullo},
journal= {arXiv preprint arXiv:2412.13906},
year = {2024}
}