Multiple error-correcting WOM-codes

A Write Once Memory (WOM) is a storage medium with binary memory elements, called cells, that can change from the zero state to the one state only once. Examples of WOMs are punch cards, optical disks, and more recently flash memories. WOM-codes were first presented by Rivest and Shamir and are designed for efficiently storing and updating data in the WOM. A WC[n, k, t] WOM-Code C_W is a coding scheme for storing k information bits in n cells t times. At each write, the state of each cell can be changed, provided that the cell is changed from the zero state to the one state. The WOM-Rate of C_W, defined to be R^t(C_W) = kt/n, indicates the total amount of information that is possible to store in a cell in t writes. Two WOM-code constructions that can correct a single cell-error were presented by Zémor and Cohen. In this paper, we present another construction of a single-error-correcting WOM-codes with a better WOM-rate. Our construction can be adjusted also for single-error-detection, double-error-correction, and triple-error-correction. For the latter case, we use triple-error-correcting BCH-like codes, which were showed by Kasami and more recently described again by Bracken and Helleseth.