Journal article
D. Bartoli, A. Davydov, M. Giulietti, S. Marcugini, F. Pambianco
Adv. Math. Commun., 2015
Adv. Math. Commun., 2015
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APA
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Bartoli, D., Davydov, A., Giulietti, M., Marcugini, S., & Pambianco, F. (2015). Further results on multiple coverings of the farthest-off points. Adv. Math. Commun.
Chicago/Turabian
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Bartoli, D., A. Davydov, M. Giulietti, S. Marcugini, and F. Pambianco. “Further Results on Multiple Coverings of the Farthest-off Points.” Adv. Math. Commun. (2015).
MLA
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Bartoli, D., et al. “Further Results on Multiple Coverings of the Farthest-off Points.” Adv. Math. Commun., 2015.
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@article{d2015a,
title = {Further results on multiple coverings of the farthest-off points},
year = {2015},
journal = {Adv. Math. Commun.},
author = {Bartoli, D. and Davydov, A. and Giulietti, M. and Marcugini, S. and Pambianco, F.}
}
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.
