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Hyper‐rook Domain Inequalities

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A hyper‐rook domain of an element x in the space (words of length n over alphabets with k elements) is a sphere with center x and fixed radius j in Hamming distance. The number j determines the dimension of the hyper‐rook domain. The classical (and far from solved) problem of covering by rook domains (here considered as the 1‐dimensional case) is the problem of finding minimal coverings of by such spheres. Very few results are known in the literature for dimensions ≥ 2. We prove in this paper certain classes of inequalities based on coverings using matrices, which give upper and lower bounds for several cases of the problem for higher dimensions.
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Document Type: Research Article

Affiliations: Universidade de Campinas, Brazil

Publication date: January 1, 1990

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