polynomial generating unit 603 begins to process the modified euclid algorithm and is in the active state at an eighth step when the second error location and analysis polynomial generating unit 603 inform the controlling unit 606 the controlling unit 606 sends a disable signal to the second switch 610 to turn off the second switch at a ninth step the first error location and analysis polynomial generating unit 602 outputs error location polynomial data and error analysis polynomial data to the error polynomial generating unit 605 and informs the controlling unit 606 about the completion of the processing of the modified euclid algorithm at the same time at a tenth step the controlling unit 606 transmits an enable signal to the first switch 609 to allow the first error location and analysis polynomial generating unit 602 to receive a next syndrome data outputted after receiving the signal informing about completion of the process from the first error location and analysis polynomial generating unit 602 at an eleventh step the first and second error location and analysis polynomial generating units 602 and 603 alternatively perform the sixth step to the tenth step repeatedly fig9 is a graph showing increment of computation complexity required to process a modified euclid algorithm as the error correction capability of the rs decoding apparatus grows in accordance with a preferred embodiment of the present invention as.