Construction of Cyclic Codes over a Class of Matrix Rings

Soham Ravikant Joshi, Shikha Patel, Om Prakash

Let ${\mathbb{F}}_2[u]/⟨u^k⟩={\mathbb{F}}_2+u{\mathbb{F}}_2+u^2{\mathbb{F}}_2+\cdots +u^{k-1}{\mathbb{F}}_2,$ where $u^k=0$ for a positive integer $k$, and $\mathcal{R}=M_4 (\mat…