Simple algorithms for decoding systematic Reed-Solomon codes
A simple algorithm for decoding nonsystematic Reed-Solomon codewords was proposed by A. Shiozaki and independently by S. Gao. We first exhibit the companion algorithm for decoding systematic Reed-Solomon codes. Next, we improve this algorithm into one that is identical to traditional Reed-Solomon decoding. The algorithm will then be adjusted to work with nonstandard Reed-Solomon codes. Finally, we modify the algorithm into one that decodes Reed-Solomon codes with erasures that is slightly more efficient than existing techniques.
reed-solomon codes euclidean algorithm erasure decoding bch codes systematic codes