Bounds on the sizes of constant weight covering codes

Motivated by applications in universal data compression algorithms we study the problem of bounds on the sizes of constant weight covering codes. We are concerned with the minimal sizes of codes of lengthn and constant weightu such that every word of lengthn and weightv is within Hamming distanced from a codeword. In addition to a brief summary of part of the relevant literature, we also give new results on upper and lower bounds to these sizes. We pay particular attention to the asymptotic covering density of these codes. We include tables of the bounds on the sizes of these codes both for small values ofn and for the asymptotic behavior. A comparison with techniques for attaining bounds for packing codes is also given. Some new combinatorial questions are also arising from the techniques.Part of this work was done while the first and third authors were visiting Bellcore. The third author was supported in part by National Science Foundation under grant NCR-8905052. Part of this work was presented in the Coding and Quantization Workshop at Rutgers University, NJ, October 1992.