# 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…

## 5 Citations

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Let $\mathrm{PG}(3,q)$ be the projective space of dimension three over the finite field with $q$ elements. Consider a twisted cubic in $\mathrm{PG}(3,q)$. The structure of the point-plane incidence…

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Upper bounds on the smallest size of a saturating set (as well as on a (1, μ)-saturating set) in the projective space PG(N, q) are obtained by using inductive constructions.

### On Cosets Weight Distribution of Doubly-Extended Reed-Solomon Codes of Codimension 4

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- 2021

It is proved that the difference between the w-th components of the distributions is uniquely determined by the Difference between the 3-rd components, which implies an interesting (and in some sense unexpected) symmetry of the obtained distributions.

### On the weight distribution of the cosets of MDS codes

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The Bonneau formula is transformed into a more structured and convenient form and it is proved that all the cosets of weight of the MDS code have the same weight distribution.

### On planes through points off the twisted cubic in PG(3, q) and multiple covering codes

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