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