Reconstruction method for Reed-Muller codes using Fast Hadamard Transform

The use of an error-correcting code is essential in communication systems where the channel is noisy. We present a new technique to reconstruct RM (Reed-Muller) codes from a noisy intercepted bit stream. RM codes have several decoding methods, including a method that uses the FHT (Fast Hadamard Transform). The FHT algorithm is composed of several butterfly operations. To verify whether or not a received code is RM, FHT is first performed assuming that the code is first-order RM. If the received code is a higher order RM other than first-order, we perform FHT after the removal of the masking components. We verified our proposed algorithm by performing intensive computer simulations.