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 ( 3 r , 2 r , 2 r ; 2 ) . Finally, a table with bounds on K ( r , s , s ; 2 ) is given.