Fast technique for computing syndromes of B.C.H. and Reed-Solomon codes

A new scheme for reducing the numerical complexity of the standard B.C.H. and Reed¿Solomon (R.S.) decoding algorithms is developed. Specifically, the process of calculating syndromes over GF(2m) is shown to require only a small fraction of the number of multiplications and additions that is required by using standard methods. As an example, the calculation of the 32 syndromes of the (255, 223, 33) Reed¿Solomon code (NASA standard for concatenation with convolutional codes) is shown to require 90% fewer multiplications and 78% fewer additions than the conventional method of computation. A computer simulation also verifies these results.