Weighted coverings and packings

: Cohen G, Honkala I, Litsyn SN, Mattson HF

Publisher: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC

: 1995

: IEEE Transactions on Information Theory

: IEEE TRANSACTIONS ON INFORMATION THEORY

: IEEE T INFORM THEORY

: 41

: 6

: 1856

: 1867

: 12

: 0018-9448

DOI: https://doi.org/10.1109/18.476311

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. The study the existence of perfect weighted codes, discuss connections between weighted coverings and packings, and present many constructions for them.

Mathematics