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We give a new method in order to obtain Weil-Serre type bounds on the minimum distance of arbitrary cyclic codes over Fpe of length coprime to p, where e ges 1 is an arbitrary integer. In an earlier paper we obtained Weil-Serre type bounds for such codes only when e =1 or e =2 using lengthy explicit factorizations, which seems hopeless to generalize. The new method avoids such explicit factorizations and it produces an effective alternative. Using our method we obtain Weil-Serre type bounds in various cases. By examples we show that our bounds perform very well against Bose-Chaudhuri-Hocquenghem (BCH) bound and they yield the exact minimum distance in some cases.