Repeated-root constacyclic codes of length ℓpsℓps and their duals

An equivalence relation is introduced on the nonzero elements of the finite field FpmFpm to classify constacyclic codes of arbitrary length over FpmFpm. According to the equivalence classes, all constacyclic codes of length ℓpsℓps over FpmFpm and their duals are characterized, where ℓℓ is a prime different from pp and ss is a positive integer. Self-dual cyclic codes of length ℓpsℓps over FpmFpm exist precisely when pp is equal to two; in this case, all self-dual cyclic codes of length 2sℓ2sℓ over F2mF2m are presented.