On constacyclic codes of length 4p^s over Fp^m + uFp^m

For any odd prime p such that p^m ≡ 1 (mod 4), the structures of all λ-constacyclic codes of length 4p^s over the finite commutative chain ring Fp^m+uFp^m (u² = 0$)$are established in terms of their generator polynomials. If the unit λ is a square, each λ-constacyclic code of length 4p^s  is expressed as a direct sum of an −α-constacyclic code and an α-constacyclic code of length 2p^s. In the main case that the unit λ is not a square, it is shown that any nonzero polynomial of degree <4 over Fp^m is invertible in the ambient ring  . When the unit λ is of the form λ = α + uβ for nonzero elements α,β of Fp^m, it is obtained that the ambient ring  is a chain ring with maximal ideal 〈x⁴ − α₀〉, and so the (α + uβ)-constacyclic codes are〈(x⁴ − α₀)ⁱ〉, for 0≤i≤2p^s. For the remaining case, that the unit λ is not a square, and λ = γ for a nonzero element γ of Fp^m , it is proven that the ambient ring  is a local ring with the unique maximal ideal〈x⁴ − γ₀,u〉. Such λ-constacyclic codes are then classified into 4 distinct types of ideals, and the detailed structures of ideals in each type are provided. Among other results, the number of codewords, and the dual of each λ-constacyclic code are provided.