Generalized Steiner Triple Systems with Group Size Ten

Generalized Steiner triple systems, GS(2, 3, n, g) are equivalent to (g+1)-ary maximum constant weight codes (n, 3,3)s. In this paper, it is proved that the necessary conditions for the existence of a GS(2,3, n, 10), namely, n ≡ 0,1 (mod 3) and n ≥ 12, are also sufficient.