The discovery of the fact that many known nonlinear codes are the Gray images of certain linear codes over Z_4, motivated the study of linear codes over rings in general. Among linear codes, the structure of linear cyclic codes and generally -cyclic codes, and among finite rings, the rings Z_{p^e} and generally finite chain rings have been more studied. In this thesis we study the structure of -cyclic codes of arbitrary length N over a finite chain ring R. In the case where R=GR(p^2,m) or R=F_{p^m}+uF_{p^m}, we o:ole="" type="#_x0000_t75" -cyclic codes of length N over R and quasi-cyclic codes of length p^{ms}N and index p^{ms-1} over F_{p^m}. By considering the ring F_{p^m}[u]/ u^{t+1} , we introduce an application of the results on the decoding of binary linear repeated-root cyclic codes of length 2N, N odd.
