Modifications to the Lagrange Interpolation Method of Decoding Reed Solomon Codes

This paper presents several modifications of the decoding algorithm for Reed Solomon codes based upon Lagrange Interpolation. One modification reduces the average number of candidate code polynomials computed and yet still achieves maximum likelihood decoding. A second modification reduces both the average and the maximuThis paper presents several modifications of the decoding algorithm for Reed Solomon codes based upon Lagrange Interpolation. One modification reduces the average number of cThis paper presents several modifications of the decoding algorithm for Reed Solomon codes based upon Lagrange interpolation. One modification reduces the average number of candidate code polynomials computed and yet still achieves maximum likelihood decoding. A second modification reduces both the average and the maximum number of candidate code polynomials computed but is no longer maximum likelihood. Decoding beyond the guaranteed error correction capability of the code is also discussed.