LAUSR

Let f(u) and g(v) be two polynomials, not both linear, which split into distinct linear factors over \(\mathbb {F}_{q}\). Let \(\mathcal {R}=\mathbb {F}_{q}[u,v]/ \langle f(u),g(v),uv-vu\rangle \) be a finite commutative non-chain ring. In this paper, we study polyadic \(\lambda \)-constacyclic codes of Type I and Type II over \(\mathcal {R}\) for \(\lambda \in \mathbb {F}_q^*\). The Gray images of polyadic negacyclic codes and their extensions lead to construction of self-dual, isodual, self-orthogonal and complementary dual(LCD) codes over \(\mathbb {F}_q\). We also study \(\alpha \)-constacyclic codes over \(\mathcal {R}\) for any unit \(\alpha \) in \(\mathcal {R}\).