Consider and for the sake of simplicity suppose for and for Then We want to compute unknowns and we could simplify the context by removing the terms. This leads to the error evaluator polynomial Thanks to we have Thanks to (the Lagrange interpolation trick) the sum degenerates to only one summand for To get we just should get rid of the product. We could compute the product directly from already computed roots of but we could use simpler form. As formal derivative we get again only one summand in So finally This formula is advantageous when one computes the formal derivative of form yielding: where Decoding based on extended Euclidean algorithm An alternate process of finding both the polynomial Λ and the error locator polynomial is based on Yasuo Sugiyama's adaptation of the Extended Euclidean algorithm. Correction of unreadable characters could be incorporated to the algorithm easily as well. Let be positions of unreadable characters. One creates polynomial localising these positions Set values on unreadable positions to 0 and compute the syndromes. As we have already defined for the Forney formula let Let us run extended Euclidean algorithm for locating least common divisor of polynomials and The goal is not to find the least common divisor, but a polynomial of degree at most and polynomials such that Low degree of guarantees, that would satisfy extended (by ) defining conditions for Defining and using on the place of in the Fourney formula will give us error values. The main advantage of the algorithm is that it meanwhile computes required in the Forney formula. Explanation of the decoding process The goal is to find a codeword which differs from the received word minimally as possible on readable positions. When expressing the received word as a sum of nearest codeword and error word, we are trying to find error word with minimal number of non-zeros on readable positions. Syndrom restricts error word by condition We could write these conditions separately or we could create polynomial and compare coefficients near powers to Suppose there is unreadable letter on position we could replace set of syndromes by set of syndromes defined by equation Suppose for an error word all restrictions by original set of syndromes hold, than New set of syndromes restricts error vector the same way the original set of syndromes restricted the error vector Except the coordinate where we have an is zero,