On two non-existence results for Cameron–Liebler k-sets in PG(n,q)

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Samenvatting

This paper focuses on non-existence results for Cameron–Liebler k-sets. A Cameron–Liebler k-set is a collection of k-spaces in or admitting a certain parameter x, which is dependent on the size of this collection. One of the main research questions remains the (non-)existence of Cameron–Liebler k-sets with parameter x. This paper improves two non-existence results. First we show that the parameter of a non-trivial Cameron–Liebler k-set in should be larger than
q^{n-5k/2-1}, which is an improvement of an earlier known lower bound. Secondly, we prove a modular equality on the parameter x of Cameron–Liebler k-sets in PG(n,q) with some restrains on (n,k,q).
In the affine case we show a similar result. This is a generalization of earlier known modular equalities in the projective and affine case.
Originele taal-2English
Aantal pagina's15
TijdschriftDesigns, Codes and Cryptography
DOI's
StatusPublished - 10 okt 2024

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© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

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