Efficient program for decoding the (255, 223) Reed-Solomon code over GF (28 ) with both errors and erasures, using transform decoding

To decode a (255, 223) Reed-Solomon code over GF(28), a fast Fourier-like transform over GF(28) has been developed to compute the syndromes and the error-erasure vectors of the transmitted code words. This new simplified transform decoder is implemented in a program on a digital computer. The (255, 223) Reed-Solomon code over GF(28) is being proposed as a NASA standard for concatenation with a (7, 1/2) conventional code. In a simulation, random code words were corrupted by random error and erasure patterns, and decoded whenever theoretically possible. A matrix of execution times for this new transform decoder under varying sets of errors and erasure patterns is included in the paper. This matrix demonstrates that the speed of the new decoder is between three and seven times faster than the software R¿¿S decoder developed previously by NASA.