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{\bf Wolfgang Haas and J\"orn Quistorff}
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{\bf On Mixed Codes with Covering Radius $1$ and Minimum Distance $2$}
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Let $R$, $S$ and $T$ be finite sets with $|R|=r$, $|S|=s$ and
$|T|=t$. A code $C\subset R\times S\times T$ with covering radius
$1$ and minimum distance $2$ is closely connected to a certain
generalized partial Latin rectangle. We present various
constructions of such codes and some lower bounds on their minimal
cardinality $K(r,s,t;2)$. These bounds turn out to be best
possible in many instances. Focussing on the special case $t=s$ we
determine $K(r,s,s;2)$ when $r$ divides $s$, when $r=s-1$, when
$s$ is large, relative to $r$, when $r$ is large, relative to $s$,
as well as $K(3r,2r,2r;2)$. Some open problems are posed. Finally,
a table with bounds on $K(r,s,s;2)$ is given.



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