Covering codes for multilevel flash memories

Write-once-memory (WOM) and flash codes are used to increase the number of writes in flash memories in order to improve the lifetime of flash-based storage systems. An early construction method of binary WOM codes used cosets of a binary linear code in the writing process, and the covering radius of the code was used to determine the number of writes possible. In this paper, we show how to combine this method with nonbinary codes for multilevel flash cells, and introduce a new family of ternary WOM codes using the finite Euclidean geometry EG(m, 3).