Clubs and their applications
Abstract
Clubs of rank k are well-celebrated objects in finite geometries introduced by Fancsali and Sziklai in 2006. After the connection with a special type of arcs known as KM-arcs, they renewed their interest. This paper aims to study clubs of rank n in PG. We provide a classification result for (n-2)-clubs of rank n, we analyze the -equivalence of the known subspaces defining clubs, for some of them the problem is then translated in determining whether or not certain scattered spaces are equivalent. Then we find a polynomial description of the known families of clubs via some linearized polynomials. Then we apply our results to the theory of blocking sets, KM-arcs, polynomials and rank metric codes, obtaining new constructions and classification results.
Keywords
Cite
@article{arxiv.2209.13339,
title = {Clubs and their applications},
author = {Vito Napolitano and Olga Polverino and Paolo Santonastaso and Ferdinando Zullo},
journal= {arXiv preprint arXiv:2209.13339},
year = {2022}
}