Further results on the covering radious of small codes

The minimum number of codewords in a code with t ternary and b binary coordinates and covering radius R is denoted by K(t,b,R). In the paper, necessary and sufficient conditions for K(t,b,R)=M are given for M=6 and 7 by proving that there exist exactly three families of optimal codes with six codewords and two families of optimal codes with seven codewords. The cases M=9 for b>=1. For ternary codes, it is shown that K(3t+2,0,2t)=9 for t>=2. New upper bounds obtained include K(3t+4,0,2t)=2. Thus, we have K(13,0,6)<=36 (instead of 45, the previous best known upper bound)