Covering and Packing Problems in Lattices Associated with then-Cube

We study optimal coverings of lattices associated with a given n -cube by frames ( = Hamming spheres of radius one) and extended frames under certain constraints, e.g., by constituting at the same time packings of the edge system in such finite lattices. These investigations also yield results on different types of packings and coverings of the n -cube by rectangular simplices whose vertices are taken from the vertex set of the cube.