Automorphisms of constant weight codes and of divisible designs (Q1974060)

After showing how to construct a constant weight code \(C(D)\) from a divisible design \(D\), the authors study how the automorphism groups of \(D\) and \(C(D)\) are related. The main result is the following: Aut\((D)\) induces a faithful group of automorphisms on \(C(D)\), which either is equal to Aut\((C(D))\) or has index equal to \(2\) in Aut\((C(D))\). In the latter case the number of points necessarily is twice the number of the block size. Besides this fundamental relation between designs and codes, the authors provide an extensive list of 28 references including many items with new results on constant weight codes which are relevant for applications.