1. A Galois Field decoder for correcting an error in a received message comprising: a. means for calculating a magnitude polynomial representing a portion of a magnitude of said error in said received message; b. means for calculating a location polynomial representing a location of said error in said received message, said location polynomial having a first derivative polynomial; c. means for calculating the first derivative polynomial of said location polynomial, said first derivative having a plurality of non-zero values, each of said non-zero values having an inverse; d. means for calculating said inverse values: e. means for multiplying each of said inverse values with a value of said magnitude polynomial for forming a correction polynomial; and f. means for correcting said received message by combining the received polynomial with the correction polynomial.