Construction and analysis of rank-modulation rewriting codes by the group of permutation matrices

In this paper, we study rank-modulation (RM) rewriting codes based on dominating sets. By introducing a special class of dominating sets in a construction of RM rewriting codes and employing the notion of a group action in an analysis of those codes, we succeeded to construct RM rewriting codes based on the dominating sets that maximize the amount of stored data under the limit of rewriting cost for flash memories with 4 and 5 cells.