  We construct many new cyclic (v;r,s;lambda) difference families with v less
than or equal 50. In particular we construct the difference families with
parameters (45;18,10;9), (45;22,22;21), (47;21,12;12), (47;19,15;12),
(47;22,14;14), (48;20,10;10), (48;24,4;12), (50;25,20;20) for which the
existence question was an open problem. The (45;22,22;21) difference family
gives a BIBD with parameters v=45, b=90, r=44, k=22 and lambda=21, and the one
with parameters (50;25,20;20) gives a pair of binary sequences of length 50
with zero periodic autocorrelation function (the periodic analog of a Golay
pair). We also construct nine new D-optimal designs. A normal form for cyclic
difference families is proposed and used effectively in compiling the list of
known and new difference families.
