The spectrum of (g., g, 3, .)-dDF in Z g.

In this paper, several recursive constructions for directed difference family and perfect directed difference family are presented by means of difference matrix and incomplete difference matrix. Finally the necessary and sufficient conditions for the existence of a (g., g, 3, .)-directed difference family in Z g. are established. As a consequence, the necessary and sufficient conditions for the existence of a cyclic directed group divisible design with block size three and type g . are obtained.