Cyclic codes of length <f>2e</f> over <f>Z4</f>

Cyclic codes of odd length over <f>Z4</f> have been studied by many authors. But what is the form of cylic codes of even length? The structure of cyclic codes of length <f>n=2e</f>, for any positive integer <f>e</f> is considered. We show that any cyclic code is an ideal in the ring <f>Rn=Z4[x]/〈xn−1〉</f>. We show that the ring <f>Rn</f> 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. [Copyright &y& Elsevier]