The covering radius of doubled 2-designs in 2Ok

The following problem originated from interconnection network considerations: what is the graphical covering radius of a doubled 2-design in the antipodal double cover of the odd graph 2Ok? In particular, when k is even, the authors take this design to be a Hadamard design. They obtain upper and lower bounds on this parameter for large values of k. The upper bound is obtained by generalizing the concept of q-covering in Johnson graphs to the graphs 2Ok. The authors use probabilistic arguments analogous to the Norse bounds of coding theory.