| Cyclic codes are an important class of linear codes. Most good linear codes can attribute to cyclic codes such as the Kerdock codes and Preparata codes which are the cyclic codes over (?)4-ring. There are comprehensive researchs on the simple root cyclic codes. But it becomes difficult to repeated-root cyclic codes, because X" -1 can not factor uniquely over a finite ring when n is not prime to the characteristic of the residue field of the ring. In this dissertation, we study repeated-root cyclic codes over the finite rings (?)2+u(?)2 and (?)2. The resultsabout codes over (?)2m+v(?)2m. are also given. The details are given as follows:1. By the discrete Fourier transforms, we get the structure of the repeated-root cyclic codes of length 2n over (?)2+u(?)2 and their dual codes. The relation ofminimum Lee-weight between the repeated-root cyclic codes and two simple-root cyclic codes is given.2. We obtain the structure of the repeated-root cyclic codes of length pkn over Z , by the discrete Fourier transforms. The number of these repeated-rootcyclic codes is also given.3. We define Gray maps from (?)2m +v(?)2m to its subrings (?)2m, (?)2' and (?)2'+v(?)2',for divisors r of m with respect to a fixed trace-orthogonal basis of (?)2. over (?)2. The results about codes over (?)2m. + vF2m. are also given.
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