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arXiv · 1506.00392

Further results on multiple coverings of the farthest-off points

Daniele Bartoli·Alexander A. Davydov·Massimo Giulietti·Stefano Marcugini·Fernanda Pambianco
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Abstract

Multiple coverings of the farthest-off points ($(R,\mu)$-MCF codes) and the corresponding $(\rho,\mu)$-saturating sets in projective spaces $PG(N,q)$ are considered. We propose and develop some methods which allow us to obtain new small $(1,\mu)$-saturating sets and short $(2,\mu)$-MCF codes with $\mu$-density either equal to 1 (optimal saturating sets and almost perfect MCF-codes) or close to 1 (roughly $1+1/cq$, $c\ge1$). In particular, we provide new algebraic constructions and some bounds. Also, we classify minimal and optimal $(1,\mu)$-saturating sets in $PG(2,q)$, $q$ small.

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Daniele Bartoli, Alexander A. Davydov, Massimo Giulietti, Stefano Marcugini, Fernanda Pambianco. 2015-06-01. Further results on multiple coverings of the farthest-off points. https://arxiv.org/abs/1506.00392

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