11. The decoding apparatus according to claim 6 wherein the means for carrying out the diagnalization process carries out a diagonalization process by using reliability levels obtained as a result of an updating process and by using an algebraic-geometry codes or codes of the same type as the algebraic-geometry codes in a finite field F (q=p m ) where p is a prime number.
13. The decoding apparatus according to claim 11 wherein the algebraic-geometry codes are Reed-Solomon codes or BCH codes, and the means for carrying out the diagonalization process carries out multiplicity-setting and soft-decision list decoding processes based on a Koetter-Vardy by taking reliability levels obtained as a result of an updating process.