Cyclotomic construction of strong external difference families in finite fields

Strong external difference families (SEDFs) and their generalizations GSEDFs and BGSEDFs in a finite abelian group G are combinatorial designs introduced by Paterson and Stinson (Discret Math 339: 2891–2906, 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. Particularly, we present an ( n , m , k , λ ) = ( 243 , 11 , 22 , 20 ) -SEDF in ( F q , + ) ( q = 3 5 = 243 ) by using the cyclotomic classes of order 11 in F q which answers an open problem raised in Paterson and Stinson ( 2016 ).