Exact hyperplane covers for subsets of the hypercube

Abstract

Alon and Füredi (1993) showed that the number of hyperplanes required to cover {0,1}n∖{0} without covering 0 is n. We initiate the study of such exact hyperplane covers of the hypercube for other subsets of the hypercube. In particular, we provide exact solutions for covering {0,1}n while missing up to four points and give asymptotic bounds in the general case. Several interesting questions are left open.