Binary number systems for image Original Research Article

For an expanding matrix image, a subset image is called a complete digit set, if all points of the integer lattice image can be uniquely represented as a finite sum image, with riset membership, variantW and image. We present a necessary and sufficient condition for the existence of a complete digit set in case det(H)=2, implying that W is a binary complete digit set. This allows a characterization of the binary number systems (H,W) in image. It is shown that, when H has a complete digit set, all its complete digit sets form a finitely generated Abelian group. Complete lists are given for dimension k=1 to 6.