Construction and nonexistence of strong external difference families.

Strong external difference families (SEDFs) were introduced by Paterson and Stinson as a more restrictive version of external difference families. SEDFs can be used to produce optimal strong algebraic manipulation detection codes. We characterize the parameters (v,m,k,λ) of a nontrivial SEDF that is near-complete (satisfying v=km+1). We construct the first known nontrivial example of a (v,m,k,λ) SEDF having m>2. The parameters of this example are (243, 11, 22, 20), giving a near-complete SEDF, and its group is Z35. We provide a comprehensive framework for the study of SEDFs using character theory and algebraic number theory, showing that the cases m=2 and m>2 are fundamentally different. We prove a range of nonexistence results, greatly narrowing the scope of possible parameters of SEDFs. [ABSTRACT FROM AUTHOR]