Further results on multiple coverings of the farthest-off points
Daniele Bartoli, Alexander A. Davydov, Massimo Giulietti, Stefano Marcugini, Fernanda Pambianco · Advances in Mathematics of Communications · 2016
Multiple coverings of the farthest-off points ($(R,\mu)$-MCF codes) and the corresponding $(\rho,\mu)$-saturating sets inprojective spa\-ces $\mathrm{PG}(N,q)$ are considered. We propose 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 closeto 1 (roughly $1+1/cq$, $c\ge1$). In particular, we providesome algebraic constructions and bounds. Also, we classifyminimal and optimal $(1,\mu)$-saturating sets in $\mathrm{PG}(2,q)$, $q$ small.