Constacyclic Codes Of Length np^s OVER F_p^m + uF_p^m

Let F_p^m be a finite field of cardinality p^m and R=F_p^m[u]/⟨u²⟩=F_p^m + uF_p^m  (u²=0), where p is a prime and m is a positive integer. For any λ ∈ F^×_p^m, an explicit representation for all distinct λ-constacyclic codes over R of length np^s is given by a canonical form decomposition for each code, where s and n are arbitrary positive integers satisfying gcd(p,n)=1. For any such code, using its canonical form decomposition the representation for the dual code of the code is provided. Moreover, representations for all distinct cyclic codes, negacyclic codes and their dual codes of length np^s over R are obtained, and self-duality for these codes are determined. Finally, all distinct self-dual negacyclic codes over F₅+uF₅ of length 2⋅3^t⋅5^s are listed for any positive integer t.