1. A method for efficiently calculating syndromes in Reed-Solomon coding, which is adapted to be implemented in a processor having a parallel processing instruction set, the method comprising the following steps: (a) initializing a syndrome vector; (b) obtaining a symbol from a Reed-Solomon block code; (c) finding a lookup index based on the symbol; (d) using the parallel processing instruction set, obtaining a finite field product vector corresponding to the lookup index from a finite field vector multiplication table that includes at least one finite field product vector; (e) using the parallel processing instruction set, performing vector finite field addition on the finite field product vector corresponding to the lookup index and the syndrome vector, thereby obtaining an updated syndrome vector; and (f) outputting the updated syndrome vector.