$(1-2u^3)$-constacyclic codes and quadratic residue codes over ${\mathbb{F}}_p[u]/⟨u^4-u⟩$

Madhu Raka, Leetika Kathuria, Mokshi Goyal

Let $\mathcal{R}={\mathbb{F}}_p+u{\mathbb{F}}_p+u^2{\mathbb{F}}_p+u^3{\mathbb{F}}_p$ with $u^4=u$ be a finite non-chain ring, where $p$ is a prime congruent to $1$ modulo $3$. In t…