In multilevel flash memories, leakage of charges results in errors, and the errors are asymmetric, of increasing type and of limited magnitude. On the other hand, low data retention may result in asymmetric errors of decreasing type and usually of smaller magnitude. Therefore, we have unbalanced error types. In this paper, some codes for correcting such errors are presented.

An error model with symmetric errors of limited magnitude is considered. Limited magnitude means that the size of any error is limited by a number smaller (usually much smaller) than the alphabet size. Several constructions of codes correcting a single error are given. In some cases, the codes are perfect or quasi- perfect.

An error model with asymmetric errors of limited magnitude is a good model for some multilevel flash memories. This paper is about constructions of codes correcting such errors. The main results are about codes correcting a single such error and codes of lengthmcorrecting all errors inm-1 or less positions.

It is an open question if there exists proper binary linear codes for error detection for all lengths and dimensions. It is known that such codes exist for any given dimension when the length is above some explicit bound. The main result in this paper is new explicit bound that is much lower than the previously known bound. The construction is based on self-complementary codes. As an illustration, proper self-complementary codes are constructed for dimensions 5 and 6 and all lengths.