Notes on Combinatorics: A New Lower Bound for Coverings by Rook Domains

摘要

Let (V sub k, sup n) be the set of all n-tuples a sub 1, a sub 2, ..., a sub n where each a sub i ranges over 0, 1, ... k-1. These can be considered as coordinate vectors of points in an n-cube with k points on a side. The Hamming metric d(x,y) is defined to be the number of coordinates in which x and y differ. A Hamming sphere about x of radius r (or a rook domain) is the set of all y in (V sub k, sup n) such that d(x,y) = or