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Cameron–Liebler k-sets in subspaces and non-existence conditions

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In this article we generalize the concepts that were used in the PhD thesis of Drudge to classify Cameron–Liebler line classes in PG(n,q),n≥3, to Cameron–Liebler sets of k-spaces in PG(n,q) and AG(n,q). In his PhD thesis, Drudge proved that every Cameron–Liebler line class in PG(n,q) intersects every 3-dimensional subspace in a Cameron–Liebler line class in that subspace. We are using the generalization of this result for sets of k-spaces in PG(n,q) and AG(n,q). Together with a basic counting argument this gives a very strong non-existence condition, n≥3k+3. This condition can also be improved for k-sets in AG(n,q), with n≥2k+2.
Tijdschrift: Des. Codes Cryptogr.
ISSN: 0925-1022
Issue: 3
Volume: 90
Pagina's: 633-651
Jaar van publicatie:2022