Cyclic Codes of Length 2e over Z4

Cyclic codes of odd length over Z4 have been studies by many outhers. But what is the form of cyclic codes of even length? The structure of cyclic codes of length 2e, for any positive integer n, is considered. We will show that any cyclic code is an ideal in the ring Rn = Z4[x]/ 〈xn − 1〉. We will show that the ring Rn is a local ring but not a principal ideal ring. Also, we will find the set of generators for cyclic codes. Examples of cyclic codes will be given.