A Reed-Solomon decoder for errors-and-erasures correction, based on a new algebraic decoding algorithm, is presented. This high-speed decoder requires onlynclock cycles for decoding each receivedn-symbol block. A serial structure that requires very few multipliers and provides a general expression to calculate the coefficients of the erasure-locator polynomial is also presented. A (15, 11) RS decoder and its shortened version (7, 3) RS decoder are used as design examples to illustrate the operating procedure of the new decoding algorithm.