APPARATUS FOR UNIFORMLY CORRECTING ERASURE AND ERROR OF RECEIVED WORD BY USING A COMMON POLYNOMIAL

A syndrome polynomial S(x) is generated based on a received word, an erasure locator polynomial .lambda.(x) is generated based on an erasure location, an error evaluator polynomial .omega.(x) is generated based on a polynomial M(x) which is a product S(x).multidot..lambda.(x) of the syndrome polynomial S(x) and the erasure locator polynomial .lambda.(x), a polynomial .tau.(x) which is a product .lambda.(x).multidot..sigma.(x) of the erasure locator polynomial .lambda.(x) and the error locator polynomial .sigma.(x) and a differentiation .tau.(x) of the polynomial .tau.(x) based on the polynomial M(x) and the erasure locator polynomial .lambda.(x), a dimension .alpha..sup.i is set to the error evaluator polynomial .omega.(x), the polynomial .tau.(x) and the differentiation .tau.'(x), and when .tau.(.alpha..sup.i)=0, the i-th symbol of the received word is corrected to .omega.(.alpha..sup.i)/.tau.'(.alpha..sup.i).