Decoding Reed-Solomon Codes Beyond Half the Minimum Distance using Shift-Register Synthesis

It is known, that interleaved Reed-Solomon codes can be decoded algebraically beyond half the minimum distance using collaborative decoding strategies. Based on the same principles, we suggest a new effective algebraic decoding method, which is able to decode a single low rate Reed-Solomon code beyond half the minimum distance. This new algorithm is based on multi-sequence shift-register synthesis, and is able to correct errors within a correcting radius similar to the Sudan algorithm. In contrast to the Sudan algorithm, which may obtain a list of codewords, our algorithm yields a decoding failure if there does not exist a unique solution. However, the probability of such a failure is very small