  Strong external difference family (SEDF) and its generalizations GSEDF,
BGSEDF in a finite abelian group $G$ are combinatorial designs raised by
Paterson and Stinson [7] in 2016 and have applications in communication theory
to construct optimal strong algebraic manipulation detection codes. In this
paper we firstly present some general constructions of these combinatorial
designs by using difference sets and partial difference sets in $G$. Then, as
applications of the general constructions, we construct series of SEDF, GSEDF
and BGSEDF in finite fields by using cyclotomic classes.
