Fast Encoding Algorithms for Reed–Solomon Codes With Between Four and Seven Parity Symbols

This article describes a fast Reed-Solomon encoding algorithm with four and seven parity symbols in between. First, we show that the syndrome of Reed-Solomon codes can be computed via the Reed-Muller transform. Based on this result, the fast encoding algorithm is then derived. Analysis shows that the proposed approach asymptotically requires 3 XORs per data bit, representing an improvement over previous algorithms. The simulation demonstrates...