On the Roth and Ruckenstein equations for the Guruswami-Sudan algorithm

In 2000 Roth and Ruckenstein proposed an extended key equation for solving the interpolation step in the Sudan decoding algorithm. Generalizing their idea, a sequence of key equations for the Guruswami-Sudan (GS) algorithm, which is able to list decode a Reed-Solomon code with arbitrary rate, is derived. This extension allows a reduction of the number of equations and therefore a reduction of the algorithmpsilas complexity. Furthermore, we indicate how to adapt the fundamental iterative algorithm for block Hankel matrices and thus solving the GS-interpolation step efficiently.