More directed GDDs with block size five
Abstract
In recent years, directed designs have been found very useful to construct perfect t-deletion/insertion-correcting codes. Directed group divisible designs (DGDDs) are instrumental in the construction of such designs. In this paper, we shall present a new recursive construction to obtain DGDDs by a variation of Wilson's construction for mutually orthogonal Latin squares. As an application, we shall improve the known results on the existence of DGDDs with blocks size five, group-type hn, and index unity. It is shown that the necessary conditions for the existence of such DGDDs, namely, n ≥ 5, (n - 1)h ≡ 0 (mod 2) and n(n - 1)h2 ≡ 0 (mod 10), are also sufficient except for (h, n) = (1, 15), and possibly excepting n = 15 and h ∈ {7, 9, 11, 13, 31, 37, 41}.
