The Reed-Solomon error-correcting circuit in accordance with a first invention is constructed so as to perform parallel operation by two-step pipelined processing in a syndrome generating circuit and an error-correcting circuit. The error-correcting circuit operates in synchronization with a clock with a period of 1/N the period of the received symbol clock, where N≧1, and N is an integer. Further, an error-locator-polynomial/error-evaluator-polynomial calculating circuit in the error-correcting circuit has a memory in which the syndrome is input and a Galois-field operations circuit that is connected to the memory. By these means, the Reed-Solomon error-correcting circuit in the present invention performs high-speed processing with small-scale hardware. Further, in an Euclid's algorithm that obtains an error-locator-polynomial, by performing Galois-field operations, from the syndrome equation S(z)=sk−1zk−1+sk−2zk−2+ . . . +s0, a second invention performs initial setting as M(z)=1, B(z)=sk−1zk−1+sk−2zk−2+ . . . +s0, and, depending on the coefficients of the syndrome equation S(z), as  A(z)=sk−2zk−1+sk−3zk−2+ . . . +s0z, L(z)=z, to reduce the number of Galois-field operations.