De Bruijn cycles for covering codes
Random Structures & Algorithms
Kolmogorov complexity with error
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
| Hi-index | 754.84 |
We prove a general recursive inequality concerning μ*(R), the asymptotic (least) density of the best binary covering codes of radius R. In particular, this inequality implies that μ*(R)≤e·(RlogR+logR+loglogR+2), which significantly improves the best known density 2RRR(R+1)/R!. Our inequality also holds for covering codes over arbitrary alphabets.