(19) United States Correcting Wom Codes, Coding Strong Single and Multiple Error Correcting Wom Codes, Coding Methods and Devices Priority Claim and Reference to Related Application

Yaakobi et al. (57) ABSTRACT Preferred embodiments of the invention provide WOM cod ing methods and electronic devices With error correcting codes that provide single, double and triple error correction. Preferred codes of the invention also the following property: if the code corrects tWo/three errors it has tWo/three parts of redundancy bits. For double error correction, if only one part of the redundancy bit has no errors then it is possible to correct one error. For triple error correction, if only one/tWo parts of the redundancy bits have no errors then it is possible to correct one/tWo errors. Preferred methods of the invention use codes that correct/ detect a single, tWo and three cell-erasures. A preferred method of the invention applies a code that has three roots, ah a2, a3, each of Which is a primitive element and Where every pair of roots generates a double error correcting code. Methods of the invention further provide and utilize codes utilitiZing a triple error correcting WOM code that can correct an arbitrary number of errors. [0001] The application claims priority under 35 U.S.C. §119 and all applicable treaties and statutes from prior pro visional application Ser.