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For any prime p, all constacyclic codes of length p s over the ring R = F p m + uF p m are considered. The units of the ring R are of the forms γ and α + uβ, where α, β, and γ are nonzero elements of F p m , which provides p m (p m − 1) such constacyclic codes. First, the structure and Hamming distances of all constacyclic codes of length p s over the finite field F p m are obtained; they are used as a tool to establish the structure and Hamming distances of all (α + uβ)-constacyclic codes of length p s over R. We then classify all cyclic codes of length p s over R and obtain the number of codewords in each of those cyclic codes. Finally, a one-to-one correspondence between cyclic and γ -constacyclic codes of length p s over R is constructed via ring isomorphism, which carries over the results regarding cyclic codes corresponding to γ -constacyclic codes of length p s over R.

We investigate negacyclic and cyclic codes of length p s over the finite field F p a . Negacyclic codes of length p s are precisely the ideals of the chain ring. This structure is then used to obtain the Hamming distance distribution of the class of such negacyclic codes, which also provides Hamming weight distributions and enumerations of several codes. An one-to-one correspondence between negacyclic and cyclic codes is established to carry accordingly those results of negacyclic codes to cyclic codes.

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