On self-dual constacyclic codes of length p^s over F_p^m + uF_p^m

The aim of this paper is to establish all self-dual λ-constacyclic codes of length p^s over the finite commutative chain ring R=F_p^m + uF_p^m, where p is a prime and u²=0. If λ = α + uβ for nonzero elements α, β of F_p^m, the ideal 〈u〉 is the unique self-dual (α + uβ)-constacyclic codes. If λ = γ for some nonzero element γ of F_p^m, we consider two cases of γ. When γ = γ⁻¹, i.e., γ = 1 or −1, we first obtain the dual of every cyclic code, a formula for the number of those cyclic codes and identify all self-dual cyclic codes. Then we use the ring isomorphism φ to carry over the results about cyclic accordingly to negacyclic codes. When γ ≠ γ⁻¹, it is shown that 〈u〉 is the unique self-dual γ-constacyclic code. Among other results, the number of each type of self-dual constacyclic code is obtained.