Quadratic residue codes over the ring ${\mathbb{F}}_p[u]/⟨u^m-u⟩$ and their Gray images

Mokshi Goyal, Madhu Raka

Let $m\ge 2$ be any natural number and let $\mathcal{R}={\mathbb{F}}_p+u{\mathbb{F}}_p+u^2{\mathbb{F}}_p+\cdots +u^{m-1}{\mathbb{F}}_p$ be a finite non-chain ring, where $u^m=u$ an…