On mixed codes with covering radius 1 and minimum distance 2: (extended abstract)

Let R, S and T be finite sets with |R|=r, |S|=s and |T|=t. A code C⊂R×S×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). Finally, a table with bounds on K(r,s,s;2) is given.