Encoding and decoding of generalized Reed-Solomon codes using parallel processing techniques

A system, computer program, and/or method for encoding data that can correct r/2 errors. The original symbols are transformed using a Fourier transform of length p. Generator polynomials are used to encode the p blocks separately, and an inverse Fourier transform is applied to obtain the redundant symbol. In a decoding system, Fourier transforms are applied to every set of p consecutive symbols of the received vector, to obtain p blocks of symbols which in total have the same size as the received vector. Next, a syndrome calculator is applied to each of these blocks to produce p syndromes. The syndromes are forwarded to a Berlekamp-Massey unit and an error locator polynomial is decimated into p parts and a Chien search is applied concurrently. A Fourier transform of length p is applied to values calculated by the Chien search, and the positions of the zeros obtained are error positions.