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
$R$
.