This M.Sc. thesis is based on the following paper Lin, T.~C., Lee, C.~D., Chen, Y.~H. and Truong, T.~K., “Algebraic decoding of cyclic codes without error-locator polynomials,” {\\em IEEE Trans. Commun.}, vol. ??, no. ?, pp. ????-????, Jul. ????. Until ????, all of which are presented for decoding BCH code associated with a polynomial to the error-locator polynomial. This dependency caused errors not to be correctly decoded as much as the error correction capacity of the BCH code. In this M.Sc. thesis, we propose a method for decoding cyclic codes with prime length, in particular BCH codes, in which not used Error-Locator polynomials, for example, the Berlekamp-Massey (BM) algorithm and the Chien's search, to identify errors in the received word. Now a q-ary cyclic code with length n (n a prime number) and the error correction capacity t is considered.
