  The root finding step of the Guruswami-Rudra list decoding algorithm for
folded Reed-Solomon codes is considered. It is shown that a multivariate
generalization of the Roth-Ruckenstein algorithm can be used to implement it.
This leads to an improved bound on the size of the list produced by the
decoder, as well as enables one to relax the constraints on the parameters of
folded codes. Furthermore, the class of time-domain folded Reed-Solomon codes
is introduced, which can be efficiently list decoded with the Guruswami-Rudra
algorithm, and provides greater flexibility in parameter selection than the
classical (frequency-domain) folded codes.
