Two New Classes of Difference Families

We construct, in a very simple way, two new classes of elementary abelian (q2, k, k−1) and (q2, k+1, k+1) difference families with k a multiple of q−1. The first of these classes contains, as special cases, the supplementary difference sys- tems constructed by A. Chaderjian (1997, J. Combin. Theory Ser. A80, 218–231).