Patent ID: 8327243

Claim:
A system comprising: a syndrome generator configured to generate a series of odd syndromes for a sequence of syndromes including even syndromes and odd syndromes; a series of registers coupled to the syndrome generator for storing the series of odd syndromes, the registers of the series of registers having a one-to-one correspondence with the odd syndromes of the series of odd syndromes; a syndrome sequencer coupled to the series of registers and configured to generate the sequence of syndromes by selecting each syndrome of the sequence of syndromes in a sequential order of the sequence of syndromes, identifying a register of the series of registers storing the selected syndrome, reading the selected syndrome from the identified register, outputting the selected syndrome for use in generating a locator polynomial, generating an even syndrome of the sequence of syndromes by squaring the selected syndrome, and replacing the selected syndrome stored in the series of registers with the even syndrome by storing the even syndrome into the register storing the selected syndrome; and a locator polynomial generator coupled to the syndrome sequencer and configured to generate the locator polynomial based on the sequence of syndromes generated by the syndrome sequencer.