  A subset V of GF(2)^n is a tile if GF(2)^n can be covered by disjoint
translates of V. In other words, V is a tile if and only if there is a subset A
of GF(2)^n such that V+A = GF(2)^n uniquely (i.e., v + a = v' + a' implies that
v=v' and a=a' where v,v' in V and a,a' in A). In some problems in coding theory
and hashing we are given a putative tile V, and wish to know whether or not it
is a tile. In this paper we give two computational criteria for certifying that
V is not a tile. The first involves impossibility of a bin-packing problem, and
the second involves infeasibility of a linear program. We apply both criteria
to a list of putative tiles given by Gordon, Miller, and Ostapenko in that none
of them are, in fact, tiles.
