  We study Euclidean designs from the viewpoint of the potential energy. For a
finite set in Euclidean space, We formulate a linear programming bound for the
potential energy by applying harmonic analysis on a sphere. We also introduce
the concept of strong Euclidean designs from the viewpoint of the linear
programming bound, and we give a Fisher type inequality for strong Euclidean
designs. A finite set on Euclidean space is called a Euclidean a-code if any
distinct two points in the set are separated at least by a. As a corollary of
the linear programming bound, we give a method to determine an upper bound on
the cardinalities of Euclidean a-codes on concentric spheres of given radii.
Similarly we also give a method to determine a lower bound on the cardinalities
of Euclidean t-designs as an analogue of the linear programming bound.
