Journal article
D. Bartoli, A. Davydov, M. Giulietti, S. Marcugini, F. Pambianco
Adv. Math. Commun., 2015
Adv. Math. Commun., 2015
Semantic Scholar
ArXiv
DBLP
DOI
Cite
Cite
APA
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
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
Bartoli, D., et al. “Further Results on Multiple Coverings of the Farthest-off Points.” Adv. Math. Commun., 2015.
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.
