Cyclic codes over ℳ_4(𝔽_2 )

In this article, keeping the huge research prospective of the study in mind, we consider the non-commutative ring ℳ_4(𝔽_2) , the set of all 4 × 4 matrices over the field 𝔽_2 and confirm that this ring is isomorphic with the ring 𝔽_16+u 𝔽_16+u^2 𝔽_16+u^3𝔽_16 , where u^4=0 . Besides, we develop the structure of cyclic codes and their generators over the ring. Also, making use of Gray map from ℳ_4(𝔽_2) to 𝔽_16^4 , we infer that the image of a cyclic code is a linear code. Finally, our findings are authenticated by suitable non-trivial examples.