| Abstract: | Constant‐weight codes (CWCs) have played an important role in coding theory. To construct CWCs, a K‐GDD (where GDD is group divisible design) with the “star” property, denoted by K‐*GDD, was introduced, in which any two intersecting blocks intersect in at most two common groups. In this paper, we consider the existence of 4‐*GDD s. Previously, the necessary conditions for existence were shown to be sufficient for  , and also sufficient for  with prime powers  and  . We continue to investigate the existence of 4‐*GDD(6n)s and show that the necessary condition for the existence of a 4‐*GDD(6n), namely,  , is also sufficient. The known results on the existence of optimal quaternary (n, 5, 4) CWCs are also extended. |
