A parallel version of a special case of the Sudan decoding algorithm

We consider the Sudan decoding algorithm of Reed-Solomon codes, in the particular case when the Y-degree of the bivariate Q(X,Y) is equal to one. It is very similar to the Welch Berlekamp algorithm. The equation for finding Q(X,Y) can be solved using an algorithm from R.R. Nielsen. Then we remark that all the univariate polynomials in these computations are of degree less than n, the length of the code, and that they can be represented by their evaluation on the support of the code. This leads to a simpler arithmetic on polynomials, which can also be parallelized. But, by the end of the process, there are unknown values at the positions of the errors, and they can be reconstructed using linear algebra.