FFT-based fast Reed-Solomon codes with arbitrary block lengths and rates

By puncturing Reed-Solomon codes with the block lengths of 2^m, it is possible to design systematic and nonsystematic codes with arbitrary block lengths and rates that can be decoded using FFT. Because Reed-Solomon (RS) codes are maximum distance separable (MDS), the resultant codes keep this property as well. The codes are constructed over prime fields as opposed to the conventional practice of extension fields, and hence additions and multiplications are simple mod operations and there is no need to use polynomials and look-up tables.