On Self-Dual Constacyclic Codes of Length 3ps over Fpm+uFpm

Let p be a prime number such that p≥5. In this paper, we classify all self-dual λ-constacyclic codes of length 3ps over the finite commutative ring R=Fpm+uFpm, where u2=0, and λ is a unit in R. For this purpose, the situation of λ is divided into two cases. First, when λ≠λ−1, we prove that there exists a unique self-dual λ-constacyclic code of length 3ps over R, namely the ideal ⟨u⟩. Second, when λ=λ−1, we establish that λ must be either 1 or −1. In this case, two subcases are considered: if pm≡1(mod3), all self-dual codes of length 3ps over R are derived from those of length ps; if pm≡2(mod3), we provide a detailed and explicit characterization of the structure of self-dual codes of length 3ps over R.