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

Abstract

Let $f(u)$ be a polynomial of degree $m,m\ge 2,$ which splits into distinct linear factors over a finite field ${\mathbb{F}}_q$. Let $\mathcal{R}={\mathbb{F}}_q[u]/⟨f(u)⟩$ be a finite non-chain ring. In an earlier paper, we studied duadic and triadic codes over $\mathcal{R}$ and their Gray images. Here, we study duadic negacyclic codes of Type I and Type II over the ring $\mathcal{R}$, their extensions and their Gray images. As a consequence some self-dual, isodual, self-orthogonal and complementary dual(LCD) codes over ${\mathbb{F}}_q$ are constructed. Some examples are also given to illustrate this.

arXiv admin note: text overlap with arXiv:1609.07862