On the covering radius 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 this paper, necessary and sufficient conditions for K(t, b, R) = M are given for all M less than or equal to 5. By the help of generalized s-surjective codes, we develop new methods for finding bounds for K(t, b, R). These results are used to prove the equality K(9, 0, 5) = 6 as well as some new lower bounds such as K(2, 7,3) greater than or equal to 7, K(3, 6, 3) greater than or equal to 8, K(5, 3, 3) greater than or equal to 8, and K(9, 0, 4) greater than or equal to 9. Some bounds for (nonmixed) quaternary codes are also obtained.