SYSTEM AND METHOD FOR GENERATING LOCATOR POLYNOMIALS

A syndrome generator generates odd syndromes of a sequence of syndromes and stores the odd syndromes in registers. A syndrome sequencer identifies the register storing the next syndrome of the sequence of syndromes, reads the syndrome from the register, and outputs the syndrome to a sequential polynomial generator. Further, the syndrome sequencer generates an even syndrome by squaring the syndrome read from the register and writes the even syndrome into the same register. Moreover, the syndrome sequencer outputs each syndrome of the sequence of syndromes in sequential order. The sequential polynomial generator generates a locator polynomial in a number of iterations based on the sequence of syndromes received from the syndrome sequencer.