This paper investigates the design and application of write-once memory (WOM)codes for flash memory storage. Using ideas from Merkx ('84), we present aconstruction of WOM codes based on finite Euclidean geometries over$\mathbb{F}_2$. This construction yields WOM codes with new parameters andprovides insight into the criterion that incidence structures should satisfy togive rise to good codes. We also analyze methods of adapting binary WOM codesfor use on multilevel flash cells. In particular, we give two strategies basedon different rewrite objectives. A brief discussion of the average-writeperformance of these strategies, as well as concatenation methods for WOM codesis also provided.
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