Constructions of ternary constant-composition codes with weight three

We consider the problem of determining the maximum size of a ternary code with constant composition and Hamming weight three. We give several constructions of codes having maximum size and we also present an improvement of the Johnson (1962) bound. The results presented solve the problem for all lengths when d=3, as well as for lengths 7, 11, and all even lengths when d=4.