منابع مشابه
Tiling Hamming Space with Few Spheres
Recently there has been some interest in the combinatorics of the geometry of the Hamming space, e.g., [10], and in particular, in tilings of this space [8]. Here, we investigate partitions of the Hamming space into spheres with possibly different radii. Such a partition is sometimes called a generalized perfect code, see e.g. [1, 3, 6, 13, 15]. Generalized spherepacking bounds can be found in ...
متن کاملGood coverings of Hamming spaces with spheres
The covering radius problem has been considered by many authors (e.g. [ 1, 5, 61). Finally, let t(n, k) be the minimum possible covering radius for an (n, k) code and k(n, p) the minimum possible dimension of a code with covering radius p. The study of t(n, k) was initiated by Karpovsky. For a survey of these questions, see ]41. The main goal of this paper is to find good linear coverings. The ...
متن کاملTiling space with notched
Stein (1990) discovered (n l)! lattice tilings of R” by translates of the notched n-cube which are inequivalent under translation. We show that there are no other inequivalent tilings of IF!” by translates of the notched cube.
متن کاملDrawing Graphs on Few Circles and Few Spheres
Given a drawing of a graph, its visual complexity is defined as the number of geometrical entities in the drawing, for example, the number of segments in a straight-line drawing or the number of arcs in a circular-arc drawing (in 2D). Recently, Chaplick et al. [4] introduced a different measure for the visual complexity, the affine cover number, which is the minimum number of lines (or planes) ...
متن کاملRep-tiling Euclidean space
A rep-tiling ~is a self replicating, lattice tiling of R". Lattice tiling means a tiling by translates of a single compact tile by the points of a lattice, and self-replicating means that there is a non-singular linear map ¢: R"-o R" such that, for each T e J, the image 4~(T) is, in turn, tiled by Y-. This topic has recently come under investigation, not only because of its recreational appeal,...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1997
ISSN: 0097-3165
DOI: 10.1006/jcta.1997.2816