2009/03/10 by Tuvi Etzion, Etzion, Tuvi
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Cellular Automata and Applications #DNA and Biological Computing #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.0903.1724
openalex publication_date 2009/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Folding a sequence S into a multidimensional box is a method that is used to construct multidimensional codes. The well known operation of folding is generalized in a way that the sequence S can be folded into various shapes. The new definition of folding is based on lattice tiling and a direction in the D-dimensional grid. There are potentially (3D-1)/(2) different folding operations. Necessary and sufficient conditions that a lattice combined with a direction define a folding are given. The immediate and most impressive application is some new lower bounds on the number of dots in two-dimensional synchronization patterns. This can be also generalized for multidimensional synchronization patterns. We show how folding can be used to construct multidimensional error-correcting codes and to generate multidimensional pseudo-random arrays.