  A subset $S$ of $k$-ary $n$-dimensional hypercube is called latin bitrade if
$|S\cap F|\in\{0,2\} $ for each 1-face $F$. We find all admissible small (less
than $2^{n+1}$) cardinalities of latin bitrades. A subset $M$ of $k$-ary
$n$-dimensional hypercube is called $t$-fold MDS code if $|M\cap F|=t $ for
each 1-face $F$. Symmetric difference of two 1-fold MDS codes is always a latin
bitrade. Symmetric difference of two $t$-fold MDS codes may also be a latin
bitrade. In this case we say that this latin bitrade embedded into $t$-fold MDS
code. The intersection of $t$-fold MDS code and a latin bitrade embedded into
it is called a component of the code. We study the questions of embedding of
latin bitrades into $t$-fold MDS and admissible cardinalities of the component
of $t$-fold MDS.
  Keywords: MDS code, latin bitrade, component.
