In this thesis , we study self-dual cyclic codes over finite fields . A linear code C of length n and dimension k over is a k- dimensional suace of the vector space over . The elements of the suace are the codewords of C and are written as or . in 2011, Jia et al . proved that Euclidean self-dual cyclic codes of length n over exist if and only if n is even and with m a positive integer . Also, they investigated the enumeration of such codes. Here we present these results. Also, we show that Hermitian self-dual cyclic codes of length n over exist if and only if n is even and with m a positive integer . Then we investigate the enumeration of such codes. The results show that the enumeration of Hermitian self-dual cyclic codes cannot be derived from that of Euclidean self-dual cyclic codes.
