Asian Research Journal of Mathematics

Let p be a prime and let R = \(\mathbb{F}_p\)m [u, v]/⟨u², v², uv−vu⟩ be a finite commutative non-chain ring with u² = v² = 0. We study ς-dual constacyclic codes of length ps over R, where ς is an automorphism of R. After explicitly characterizing the unit group of R and the full automorphism group Aut(R), we determine all admissible constacyclic shift constants λ. Exploiting the idea structure of R[x]/⟨xp^s − λ⟩, we derive generator polynomials for C^⊥ς in both the principal and non-principal cases—a distinction that arises precisely because R is non-chain. Because R is a non-chain ring, the ideal structure of the associated quotient ring gives rise to both principal and non-principal ideals, and we treat both cases separately, deriving explicit generator polynomials for each. We establish necessary and sufficient conditions on λ and ς for ς-self-dual codes to exist. These results generalize and unify prior work on constacyclic codes over chain rings such as \(\mathbb{F}_p\)m [u]/⟨u^k⟩, and yield new families of constacyclic codes with prescribed duality properties.