Simplified algorithm for correcting both errors and erasures of Reed-Solomon codes

Abstract

Using a finite-field transform, a simplified algorithm for decoding Reed-Solomon codes is developed to correct erasures as well as errors over the finite-field GF(q to the m power), where q is a prime and m is an integer. If the finite-field transform is a fast transform, this decoder can be faster and simpler than a decoder that uses more conventional methods.