A method of decoding a one-point algebraic geometric code of dimension k and length n, in which, in order to identify the position of the errors in a received word, the syndromes matrix S, of size (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. Matrices S.sup.u are constructed for the successive values of u starting with S.sup.1=S, and, for u>1, each matrix S.sup.u is obtained by performing on the matrix S.sup.u-1, column permutations where appropriate, then linear manipulations involving the line of index u. These steps are performed in such a manner as to find a matrix S.sup..lamda. which has a line of index less than or equal to .lamda. of which the elements are zero in the first w(.lamda.) columns. The invention also relates to devices and apparatuses adapted to implement this method.