Binary Covering Arrays and Existentially Closed Graphs

On Symmetric Designs and Binary 3-Frameproof Codes

“…u t Remark. For all primes q Á 3 mod 4, q > 1;024, it is noted in Colbourn and Kéri [5] that Paley difference sets yield covering arrays of strength four, which immediately implies that they are f1; 3g-SHFs. This follows from a similar character-theoretic argument.…”

Using Grid Computing for Constructing Ternary Covering Arrays

“…Zero-sum leads to CA(v t ; t, t + 1, v) for any t > 2; note that the value of degree is in function of the value of strength. Recently, cyclotomic classes based on Galois finite fields have been shown to provide examples of binary CAs, and more generally examples are provided by certain Hadamard matrices (Colbourn & Kéri, 2009). …”

A Survey of Binary Covering Arrays

“…It appears in Table 2. Subsequently, Colbourn and Kéri [29] discovered a simple construction for such an array.…”

“…Colbourn and Kéri [29] study the relationship between binary covering arrays and existentially closed graphs. A t-existentially closed graph is a graph such that, whenever sets A, B form a partition of a set of t vertices of the graph, there is a vertex v not in A ∪ B such that each vertex in A is adjacent to v, while no vertex of B is adjacent to v. The adjacency matrix of a t-existentially closed graph with k vertices is an element of CA(k, k, t).…”