Method and apparatus for decoding a one-point algebraic geometric code of dimension k and length n, in order to identify the position of the errors in a received word, the syndromes matrix S, of dimension (n-k).times.(n-k) is defined, of which the elements S.sub.ij of each line i are calculated, for j between 1 and w(i), where the boundary w is a decreasing function, using the syndrome s of the received word, as well as the matrix S* obtained by "extending" the matrix S, that is to say by calculating the value of certain elements S*.sub.ij where j is greater than w(i). This method makes it possible in certain favorable cases to find the erroneous positions of the received word when the number of errors is greater than (n-k+1-g)/2, even if it is not possible to calculate all the elements of S* conventionally required by a two-stage algorithm to perform that correction.