Floating codes with good average performance

Floating codes are codes for multi-level flash memories. There are two main properties which those codes have, the worst-case block erasure period and the average block erasure period. Codes with large average block erasure period can be constructed from the Gray code. First it is shown that a construction method for the floating codes can be interpreted by using labelled graphs. Floating codes are proposed for cases (a) n = 5 and k = 4, l = 2, q >; 2; (b) n = 8, k = 4, I = 2, q>; 2, where n is the number of cells in a block, k the number of information variables, I the number of levels of information variables and q the number of levels of cells. It is shown that if input data do not distribute uniformly, then the frequency of block erasure is low when the proposed code is used.