Local distributions for eigenfunctions and for perfect colorings of q-ary hypercube

Abstract

Under study are the eigenfunctions and perfect colorings of the graph of $n$-dimensional $q$-ary Hamming space. We obtain the interdependence of local distributions of an eigenfunction in two orthogonal faces. We prove also an analogous result for perfect colorings.

8 pages. The results in the paper were published in part at the Seventh International Workshop on Optimal Codes and Related Topics, September 2013