A note on multiple coverings of the farthest-off points
نویسندگان
چکیده
In this work we summarize some recent results, to be included in a forthcoming paper [1]. We define μ-density as a characteristic of quality for the kind of coverings codes called multiple coverings of the farthest-off points (MCF). A concept of multiple saturating sets ((ρ, μ)-saturating sets) in projective spaces PG(N, q) is introduced. A fundamental relationship of these sets with MCF is showed. Bounds for the smallest possible cardinality of (1, μ)-saturating sets are obtained. Constructions of small (1, μ)-saturating sets improving the probabilistic bound are proposed.
منابع مشابه
Further results on multiple coverings of the farthest-off points
Multiple coverings of the farthest-off points ((R,μ)-MCF codes) and the corresponding (ρ, μ)-saturating sets in projective spaces PG(N, q) are considered. We propose some methods which allow us to obtain new small (1, μ)-saturating sets and short (2, μ)-MCF codes with μ-density either equal to 1 (optimal saturating sets and almost perfect MCF-codes) or close to 1 (roughly 1+1/cq, c ≥ 1). In par...
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ورودعنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 40 شماره
صفحات -
تاریخ انتشار 2013