On the covering radius of codes

Designing a good error-correcting code is a packing problem. The corresponding covering problem has received much less attention: now the codewords must be placed so that no vector of the space is very far from the nearest codeword. The two problems are quite different, and with a few exceptions good packings, i.e. codes with a large minimal distance, are usually not especially good coverings. The recent survey of Cohen, Karpovsky, Mattson and Schatz [8] gives an excellent summary of earlier work, as well as a number of new results. (A recent Soviet paper [19], not mentioned in [8], studies codes of very high rate.)