Strong single and multiple error correcting WOM codes, coding methods and devices

摘要

The invention provides WOM coding methods and electronic devices with error correcting codes that provide single, double and triple error correction. In one coding, 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. Codes that correct/detect a single, two and three cell-erasures are provided. A code that has three roots, α₁, α₂, α₃, each of which is a primitive element and where every pair of roots generates a double error correcting code, is provided. Codes and coding utilizing a triple error correcting WOM code that can correct an arbitrary number of errors are provided.