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arXiv · 2412.13906

Whitney Numbers of Rank-Metric Lattices and Code Enumeration

Giuseppe Cotardo·Alberto Ravagnani·Ferdinando Zullo
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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.

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Giuseppe Cotardo, Alberto Ravagnani, Ferdinando Zullo. 2024-12-18. Whitney Numbers of Rank-Metric Lattices and Code Enumeration. https://arxiv.org/abs/2412.13906

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