  A subset $S$ of $\{0,1,...,2t-1\}^n$ is called a $t$-fold MDS code if every
line in each of $n$ base directions contains exactly $t$ elements of $S$. The
adjacency graph of a $t$-fold MDS code is not connected if and only if the
characteristic function of the code is the repetition-free sum of the
characteristic functions of $t$-fold MDS codes of smaller lengths.
  In the case $t=2$, the theory has the following application. The union of two
disjoint $(n,4^{n-1},2)$ MDS codes in $\{0,1,2,3\}^n$ is a double-MDS-code. If
the adjacency graph of the double-MDS-code is not connected, then the
double-code can be decomposed into double-MDS-codes of smaller lengths. If the
graph has more than two connected components, then the MDS codes are also
decomposable. The result has an interpretation as a test for reducibility of
$n$-quasigroups of order 4. Keywords: MDS codes, n-quasigroups,
decomposability, reducibility, frequency hypercubes, latin hypercubes
