# Higgledy-piggledy sets in projective spaces of small dimension

@inproceedings{Denaux2021HiggledypiggledySI, title={Higgledy-piggledy sets in projective spaces of small dimension}, author={Lins Denaux}, year={2021} }

This work focuses on higgledy-piggledy sets of k-subspaces in PG(N, q), i.e. sets of projective subspaces that are ‘well-spread-out’. More precisely, the set of intersection points of these k-subspaces with any (N − k)-subspace κ of PG(N, q) spans κ itself. We highlight three methods to construct small higgledy-piggledy sets of k-subspaces and discuss, for k ∈ {1, N − 2}, ‘optimal’ sets that cover the smallest possible number of points. Furthermore, we investigate small non-trivial higgledy…

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Upper bounds on the length function for covering codes

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New upper bounds on `q(tR + 1, R) are obtained in the following forms: q is an arbitrary prime power, c is independent of q, and q is large enough.

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