Hefftner, White, Alpert, and others observed a connection between topology and certain block designs with parameters k = 3 and ,I= 2. In this paper the connection is extended to include all values of I.. The topology is also exploited further to produce some new invariants of designs. The topology also gives an upper bound for the order of the automorphism group of the designs studied which lea...

We consider strong external difference families (SEDFs); these are external difference families satisfying additional conditions on the patterns of external differences that occur, and were first defined in the context of classifying optimal strong algebraic manipulation detection codes. We establish new necessary conditions for the existence of (n,m, k, λ)-SEDFs; in particular giving a near-co...

We give a quadratic O(|X|) space representation based on a canonical tree for any subset family F ⊆ 2 holding the closure under union and difference of overlapping members. The cardinal of F is potentially in O(2), and its size higher. As far as we know this is the first representation theorem for such families. As an application of this framework we obtain a uniqueness decomposition theorem on...

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 differe...