Further results on the covering radius of small codes Original Research Article

The minimum number of codewords in a code with t ternary and b binary coordinates and covering radius R is denoted by image. In the paper, necessary and sufficient conditions for image are given for image 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 image were settled in an earlier study by the same authors. For binary codes, it is proved that image for image. For ternary codes, it is shown that image for image. New upper bounds obtained include image for image. Thus, we have image (instead of 45, the previous best known upper bound).