rs since not all the words of symbols are possible code words, but only a subset of Mm words are acceptable. Thus, when an unacceptable word is detected, errors are revealed and, starting from the received word, an algorithm exists to estimate the transmitted word. The number of nonzero symbols in the difference between two words of symbols in G(M) is called distance between the words and it is possible to verify that it has all the properties of a well-defined distance. The minimum distance between two code words is called Hamming distance of the code and it is quite clear that the upper bound of the number of errors that the code can correct is exactly the Hamming distance. As a matter of fact, changing a number of symbols equal to the Hamming distance is possible to change a code word into another code word, creating an error that is impossible to correct. The Galois fields that are used in the block codes commonly used in optical transmis- sion are the fields constituted by the integer numbers module for a given field-generating Telecommunication Networks number so which has to be a prime or the power of a prime; such fields are called ((s). As an example, G(5) = {0, 1, 2, 3, 4}, where all the numbers have to be an intended module 5, SO that, within G(5), 4+3 = 2 mod(5). The symbols of the alphabet M are considered elements of G(M) SO as to be able to per- form operations with them. On the grounds of this definition, every word is represented with a polynomial in G(M), associating to the finite sequence of symbols Xj,j=1,..., d} the polynomial P(y)= With this definition, encoding and decoding algorithms can be structured as an opera- tion with polynomials on G(M), the type of operation that a dedicated logic like that of an ASIC or of a DSP executes very fast. Different codes can be defined depending on the encoding and decoding algorithms; each code is characterized by a correction capability (number of independent errors the code can correct in a received word), a detection capability (number of errors the 