On boolean functions with the sum of every two of them being bent

A set of Boolean functions is called a bent set if the sum of any two distinct members is a bent function. We show that any bent set yields a homogeneous system of linked symmetric designs with the same design parameters as those systems derived from Kerdock sets. Further we observe that there are bent sets of size equal to the square root of the Kerdock set size which consist of Boolean functions with arbitrary degrees.