Cross-Error Correcting Integer Codes over ${\mathbb{Z}}_{2^m}$

In this work we investigate codes in ${\mathbb{Z}}_{2^m}^n$ that can correct errors that occur in just one coordinate of the codeword, with a magnitude of up to a given parameter $t$. We will show upper bounds on these cross codes, derive constructions for linear codes and respective decoding algorithm. The constructions (and decoding algorithms) are given for length $n=2$ and $n = 3$,butforgeneral$m$and$t$.