Good coverings of Hamming spaces with spheres

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Good 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 ...

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On the Thinnest Coverings of Spheres and Ellipsoids with Balls in Hamming and Euclidean Spaces

In this paper, we present some new results on the thinnest coverings that can be obtained in Hamming or Euclidean spaces if spheres and ellipsoids are covered with balls of some radius ε. In particular, we tighten the bounds currently known for the ε-entropy of Hamming spheres of an arbitrary radius r. New bounds for the ε-entropy of Hamming balls are also derived. If both parameters ε and r ar...

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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 ...

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 1985

ISSN: 0012-365X

DOI: 10.1016/0012-365x(85)90020-2