Result: Whitney numbers of rank-metric lattices and code enumeration.

Title:
Whitney numbers of rank-metric lattices and code enumeration.
Authors:
Cotardo, Giuseppe1 (AUTHOR) gcotardo@vt.edu, Ravagnani, Alberto1,2 (AUTHOR), Zullo, Ferdinando1,3 (AUTHOR)
Source:
Advances in Applied Mathematics. Dec2025, Vol. 171, pN.PAG-N.PAG. 1p.
Subject Terms:
*LATTICE theory, *CODING theory, *COMBINATORIAL enumeration problems, *VECTOR spaces, *COMBINATORIAL designs & configurations, *ASYMPTOTIC analysis, *MATHEMATICAL functions
Database:
Academic Search Index

Further Information

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. [ABSTRACT FROM AUTHOR]