• Journal of Advanced Navigation Technology
• /
• v.15 no.5
• /
• pp.781-788
• /
• 2011

A sphere-packing problem is to find an arrangement of the spheres to fill as large area of the given space as possible, and covering problems are optimization problems which are dual problems to the packing problems. We generalize the concepts of the weight and the Hamming distance for a binary code to those of Boolean algebra. In this paper, we define a weight and a distance on a Boolean algebra and research some properties of the weight and the distance. Also, we prove the notions of the sphere-packing bound and the Gilbert-Varshamov bound on Boolean algebra.