Bounds on Covering Radius of Some Codes Over F₂ + uF₂ + vF₂ + uvF₂

Let $R=\mathbb {F}_{2}+u\mathbb {F}_{2}+v\mathbb {F}_{2}+uv\mathbb {F}_{2}$ be a finite non-chain ring, where $u^{2}=u$ , $v^{2}=v$ , $uv=vu$ . We give the lower and upper bounds on the covering radius of different types of repetition codes for Chinese Euclidean distance over $R$ . Furthermore, we determine the upper bound on the covering radius of block repetition codes, simplex codes of types $\alpha $ and $\beta $ , MacDonald codes of types $\alpha $ and $\beta $ for Chinese Euclidean distance over $R$ .