Abstract: An apparatus and method for decoding data encoded in a linear cyclic code with less hardware than the prior art decoding apparatus without sacrificing the processing speed are described. The polynomial arithmetic part 14 derives polynomials &sgr;(x), &ohgr;(x) by repeating calculation of the following Qi(x), exchange of polynomials between the register U_reg 180 and the register X_reg 184, and exchange of polynomials between the register Y_reg 182 and the register Z_reg 186 until the degree (deg Xreg) of the polynomial in the register X_reg 184 becomes smaller than [(d−h+1)/2] to solve the following recursive formula.