Maximal families of bent sequences

In a recent paper Olsen, Scholtz, and Welch (OSW) describe the use of bent functions to construct families of sequences with asymptotically optimal correlation properties. We show that the sequences produced by the OSW construction possess the claimed correlation properties if and only if the underlying bent functions are pairwise orthogonal. Consequently, the cardinality of a family of OSW sequences of length
2^{n}-1
cannot exceed
2^{n/2}
. We also describe methods of selecting a maximal set of orthogonal bent functions.