Bounds on the linear span of bent sequences

The Olsen et al (1982) 'bent function' families of binary sequences, which can be generated through nonlinear operations on m-sequences, possess asymptotically optimum correlation properties and large equivalent linear span (ELS) values. Upper and lower bounds to the ELS of bent function sequences are derived, and the upper bound is found to improve on Key's (1976) result. An interesting general result contained in the derivation is the exhibition of a class of nonlinear sequences whose ELS is guaranteed to be large.