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Let $f(u)$ be a polynomial of degree $m, m \geq 2,$ which splits intodistinct linear factors over a finite field $\mathbb{F}_{q}$. Let$\mathcal{R}=\mathbb{F}_{q}[u]/\langle f(u)\rangle$ be a finite non-chain ring.In an earlier paper, we studied duadic and triadic codes over $\mathcal{R}$ andtheir Gray images. Here, we study duadic negacyclic codes of Type I and Type IIover the ring $\mathcal{R}$, their extensions and their Gray images. As aconsequence some self-dual, isodual, self-orthogonal and complementarydual(LCD) codes over $\mathbb{F}_q$ are constructed. Some examples are alsogiven to illustrate this.

Duadic negacyclic codes over a finite non-chain ring and their Gray images