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Binary Non-tiles | | Don Coppersmith
; Victor S. Miller
; | | Date: |
7 Nov 2009 | | Abstract: | 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. | | Source: | arXiv, 0911.1388 | | Services: | Forum | Review | PDF | Favorites | |
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