Cyclic codes of length 2e over Z4 Original Research Article

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