Cyclic And Negacyclic Codes Over The Residue Rings

In this thesis, we study the structure of linear codes over the ring of integers modulo m. We first give the structure of negacyclic codes over the p-adic integers, then we discuss the image of the constacyclic codes under the projection map (?)_e^f, where (?)_e^f : Z_p^f→Z_p^e,a(?)a (mod e). Furthermore, the structure of cyclic codes and its dual codes under the projection (?)_e^f is given. Finally, by using Fourier transform, the structure of negacyclic codes of even length over Z_2^k is investigated, and by the definition of generalized Gray map, the image of negacyclic codes of length 2^s over Z_2^k under the Gray map is discussed.