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Horst Martini; Walter Wenzel : Covering and Packing Problems in Lattices associated with the n-Cube

Horst Martini; Walter Wenzel : Covering and Packing Problems in Lattices associated with the n-Cube

Author(s) :
Horst Martini; Walter Wenzel
Title :
Covering and Packing Problems in Lattices associated with the n-Cube
Preprint series
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 2000-4, 2000
Mathematics Subject Classification :
52C07 [ Lattices and convex bodies in n dimensions ]
52C17 [ Packing and covering in n dimensions (discrete geometry) ]
94B05 [ General theory of linear codes ]
Abstract :
Optimal coverings of lattices associated with a given n-cube by Hamming spheres of radius one are studied where certain constraints are taken into consideration. These investigations also yield results about packings of the n-cube by rectangular simplices whose vertices should cover the vertex set of the n-cube.
Keywords :
Coding theory, covering problem, n-dimensional cube, cubical lattice, Hamming distance, linear codes, packing problem, prime power, simplex,
Language :
english
Publication time :
4/2000