Cyclic codes over GR(p2,m) of length pk

We study cyclic codes of length pk over GR(p2,m), or equivalently, ideals of the ring GR(p2,m)/〈upk−1〉. We derive a method of representing the ideals, and classify all ideals in the ring GR(p2,m)/〈upk−1〉. We also analyse the duals, and identify the self-dual ideals.