Further results on multiple coverings of the farthest-off points

@article{Bartoli2015FurtherRO,
  title={Further results on multiple coverings of the farthest-off points},
  author={Daniele Bartoli and Alexander A. Davydov and Massimo Giulietti and Stefano Marcugini and Fernanda Pambianco},
  journal={Adv. Math. Commun.},
  year={2015},
  volume={10},
  pages={613-632}
}
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… 

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