Cones from maximum h-scattered linear sets and a stability result for cylinders from hyperovals

Sam Adriaensen, Jonathan Mannaert, Ferdinando Zullo, Paolo Santonastaso

Onderzoeksoutput: Articlepeer review

Samenvatting

This paper mainly focuses on cones whose basis is a maximum h-scattered linear set. We start by investigating the intersection numbers of such cones with respect to the hyperplanes. Then we analyze two constructions of point sets with few intersection numbers with respect to the hyperplanes. In particular, the second one extends the construction of translation KM-arcs in projective spaces, having as part at infinity a cone with basis a maximum h-scattered linear set. As an instance of the second construction we obtain cylinders with a hyperoval as basis, which we call hypercylinders, for which we are able to provide a stability result. The main motivation for these problems is related to the connections with both Hamming and rank distance codes. Indeed, we are able to construct codes with few weights and to provide a stability result for the codes associated with hypercylinders.

Originele taal-2English
Artikelnummer113602
Aantal pagina's19
TijdschriftDiscrete Mathematics
Volume346
Nummer van het tijdschrift12
DOI's
StatusPublished - dec 2023

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© 2023 The Author(s)

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