On Systematic Generator Matrices for Reed–Solomon Codes
D.J.J. Versfeld, James N. Ridley, Hendrik Christoffel Ferreira, Albert S. J. Helberg · IEEE Transactions on Information Theory · 2010
We derive a simple formula to generate a wide-sense systematic generator matrixBfor a Reed-Solomon code. Specifically, we generate the generator matrixBsuch that the columns with indices ¿1, ¿2,..., ¿kare the columns of the identity matrixIk. One possible application of these wide-sense matrices is erasures-only decoding.