Combinatorial codes, Coverings, Perfect codes, Constructions of codes.
In this paper we introduce a generalization of the concepts of coverings and packings in Hamming space called weighted coverings and packings. This allows us to formulate a number of well-known coding theoretical problems in a uniform manner. We study the existence of perfect weighted codes, discuss connections between weighted coverings and packings, and present many constructions for them.
Cohen, G. D.; Honkala, Iiro; Litsyn, S. N.; and Mattson, H. F. Jr, "Weighted Coverings and Packings" (1995). Electrical Engineering and Computer Science - Technical Reports. 140.