SOME CLASSES OF REPEATED-ROOT CONSTACYCLIC CODES OVER Fpm + uFpm + u2Fpm
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Constacyclic codes of length ps over R = Fpm + uFpm + u2Fpm are precisely the ideals of the ring R[x]/(xps −1). In this paper, we investigate constacyclic codes of length ps over R. The units of the ring R are of the forms γ, α+uβ, α+uβ +u2γ and α+u2γ, where α, β and γ are nonzero elements of Fpm . We obtain the structures and Hamming distances of all (α+uβ)-constacyclic codes and (α+uβ+u2γ)-constacyclic codes of length ps over R. Furthermore, we classify all cyclic codes of length ps over R, and by using the ring isomorphism we characterize γ-constacyclic codes of length ps over R.
Abstract
Constacyclic codes of length ps over R = Fpm + uFpm + u2Fpm are precisely the ideals of the ring R[x]/(xps −1). In this paper, we investigate constacyclic codes of length ps over R. The units of the ring R are of the forms γ, α+uβ, α+uβ +u2γ and α+u2γ, where α, β and γ are nonzero elements of Fpm . We obtain the structures and Hamming distances of all (α+uβ)-constacyclic codes and (α+uβ+u2γ)-constacyclic codes of length ps over R. Furthermore, we classify all cyclic codes of length ps over R, and by using the ring isomorphism we characterize γ-constacyclic codes of length ps over R.
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