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Constacyclic codes of length p s over R = Fpm + uFpm + u2Fpm are precisely the ideals of the ring R(x) hxp s −1i . In this paper, we investigate constacyclic codes of length p s over R. The units of the ring R are of the forms , +u, +u +u 2 and +u 2 , where ,  and are nonzero elements of Fpm. We obtain the structures and Hamming distances of all (+u)-constacyclic codes and (+u+u 2 )-constacyclic codes of length p s over R. Furthermore, we classify all cyclic codes of length p s over R, and by using the ring isomorphism we characterize -constacyclic codes of length p s over R.

SOME CLASSES OF REPEATED-ROOT CONSTACYCLIC CODES OVER 𝔽pm+u𝔽pm+u2𝔽pm

SOME CLASSES OF REPEATED-ROOT CONSTACYCLIC CODES OVER 𝔽_p_m+u𝔽_p_m+u²𝔽_p_m