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Let p ≠ 3 be any prime. The algebraic structures of all λ -constacyclic codes of length 3 p s over the finite commutative chain ring R = F p m + u F p m are provided by classifying all ideals of the local ring R [ x ] 〈 x 3 p s − λ 〉. Using these structures, in this paper, the exact values of Hamming distances of all such λ -constacyclic codes of length 3 p s are established. As an application, we identify all maximal distance separable λ -constacyclic codes of length 3 p s. [ABSTRACT FROM AUTHOR]

The units of the chain ring R a = F p m [ u ] 〈 u a 〉 = F p m + u F p m + ⋯ + u a − 1 F p m are partitioned into a distinct types. It is shown that for any unit Λ of Type k , a unit λ of Type k ∗ can be constructed, such that the class of λ -constacyclic of length p s of Type k ∗ codes is one-to-one correspondent to the class of Λ -constacyclic codes of the same length of Type k via a ring isomorphism. The units of R a of the form Λ = Λ 0 + u Λ 1 + ⋯ + u a − 1 Λ a − 1 , where Λ 0 , Λ 1 , … , Λ a − 1 ∈ F p m , Λ 0 ≠ 0 , Λ 1 ≠ 0 , are considered in detail. The structure, duals, Hamming and homogeneous distances of Λ -constacyclic codes of length p s over R a are established. It is shown that self-dual Λ -constacyclic codes of length p s over R a exist if and only if a is even, and in such case, it is unique. Among other results, we discuss some conditions when a code is both α - and β -constacyclic over R a for different units α , β . [ABSTRACT FROM AUTHOR]