On a Singular Value Problem for the Fractional Laplacian on the Exterior of the Unit Ball

2000 Mathematics Subject Classification: Primary 26A33; Secondary 47G20, 31B05

Distance Distributions and Energy of Designs in Hamming Spaces

We obtain new combinatorial upper and lower bounds for the potential energy of designs in q-ary Hamming space. Combined with results on reducing the number of all feasible distance distributions of such designs this gives reasonable good bounds. We compute and compare our lower bounds to recently obtained universal lower bounds. Some examples in the binary case are considered.