A POLYNOMIAL DIVIDER WHICH CAN PERFORM EUCLID'S ALGORITHM TO PRODUCE AN ERROR LOCATOR POLYNOMIAL FROM AN ERROR SYNDROME POLYNOMIAL, AND APPARATUS INCLUDING THE POLYNOMIAL DIVIDER

摘要

A polynomial divider which can perform Euclid's Algorithm by iteratively solving both equations thereof through performing iterations of polynomial division so as to produce an error locator polynomial from an error syndrome polynomial, and apparatus including the polynomial divider. The polynomial divider is capable of performing polynomial division of a numerator polynomial by a denominator polynomial to produce a quotient polynomial and a remainder polynomial. The polynomial divider includes (a) a first set of registers for storing the denominator polynomial; (b) a second set of registers for storing the remainder polynomial; (c) an input for receiving the numerator polynomial; (d) an output for supplying the quotient polynomial; (e) a first coupling unit for coupling the first set of registers to the input so that the denominator polynomial stored in the first set of registers becomes the numerator polynomial which is received by the input and used in a further polynomial division; and (f) a second coupling unit for coupling the second set of registers to the first set of registers so that the remainder polynomial stored in the second set of registers becomes the denominator polynomial which is stored in the first set of registers and used in the further polynomial division. An error locator polynomial determining apparatus includes the polynomial divider and a control unit for controlling the polynomial divider. An error correction apparatus includes the error locator polynomial determining apparatus, an error information determiner and a data corrector.