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

An n-dimensional chair consists of an n-dimensional box from which a smaller n-dimensional box is removed. A tiling of an n-dimensional chair has two nice applications in some memories using asymmetric codes. The first one is in the design of codes which correct asymmetric errors with limited-magnitude. The second one is in the design of n cells q-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 an n-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.