On non-linear codes correcting errors of limited size

The writing operation of multi-level flash memories can suffer from voltage overshoots, which can be generally modeled as asymmetric errors of limited magnitude. Using suitable error correcting codes, these kinds of errors can be corrected. In particular, -ary non-linear codes of length 2 are equivalent to packings of the plane modulo with quasi-crosses. The design procedures for a number of such packings are presented