Abstract: In a decoding system of an error correction code, a mixed correction of, for example, a one-extended Reed-Solomon code at one path is made possible. The number &egr; of erasures and an erasure position polynomial E(x) are obtained from an erasure flag F including an extended erasure flag F−. A syndrome polynomial S(x) is obtained from a received word R including an extended received symbol R−, a modified syndrome polynomial Sm(x) is obtained from the polynomials E(x) and S(x), and an error evaluator polynomial &ohgr;(x) and an error locator polynomial &sgr;(x) are obtained from the Sm(x). An error position i is detected from &sgr;(x). An error value ei at a position i is calculated from &ohgr;(x), &sgr;(x) and the error position i, an extended error value e− is calculated from this error value ei and the 0th element S0 of the syndrome S, and further, presumed information Ip is obtained from the received word R, the error position i, the error value ei, and the extended error value e−.