Tilings With n-Dimensional Chairs and Their Applications to Asymmetric Codes

Ann-dimensional chair consists of ann-dimensional box from which a smallern-dimensional box is removed. A tiling of ann-dimensional chair has two nice applications in some memories using asymmetric codes. The first one is in the design of codes that correct asymmetric errors with limited magnitude. The second one is in the design ofncellsq-ary write-once memory codes. We show an equivalence between the design of a tiling with an integer lattice and the design of a tiling from a generalization of splitting (or of Sidon sequences). A tiling of ann-dimensional chair can define a perfect code for correcting asymmetric errors with limited magnitude. We present constructions for such tilings and prove cases where perfect codes for these type of errors do not exist.