Polyadic constacyclic codes over a non-chain ring $$\mathbb {F}_{q}[u,v]/\langle f(u),g(v), uv-vu\rangle $$

Abstract

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 $$\mathcal {R}$$.