We construct, in a very simple way, two new classes of elementary abelian (
q(2), k, k - 1) and (q(2), k + 1, k + 1) difference families with ic a mult
iple of q - 1. The first of these classes contains, as special cases, the s
upplementary difference systems constructed by A. Chaderjian (1997, J. Comb
in. Theory Ser. A 80, 218-231). (C) 2000 Academic Press.