Abstract: This specification covers a simplified and high speed decoding scheme for Reed-Solomon codes capable of correcting up to three symbol errors in code words made up of k data and n-k check symbols where each symbol consists of m binary bits of information. In such a code the error location polynomial .sigma. (x) = x.sup.e + .sigma..sub.1 x.sup.e-1 . . . . .sigma..sub.e where e equals the number of symbol errors and the coefficient of .sigma.(x) are related to the error syndromes S.sub.i by the equationS.sub.i+e + .sigma..sub.1 S.sub.i+e-1 +. . . . + .sigma..sub.e-1 S.sub.i+1 + .sigma..sub.e S.sub.i = 0.The decoder first tests if S.sub.0 = 0. If S.sub.0 .noteq. 0, the assumption is made that a single symbol error has occurred. The decoder quickly verifies this by determining if S.sub.2 + .sigma.S.sub.1 = 0 and S.sub.3 + .sigma.S.sub.2 = 0 when .sigma. = S.sub.1 /S.sub.0.