Bounds on the linear span of bent sequences

Recently, Olsen, Scholtz, and Welch presented families of binary sequences called bent-function sequences which can be generated through nonlinear operations on
m
-sequences. These families of sequences possess asymptotically optimum correlation properties and large equivalent linear span (ELS). Upper and lower bounds to the ELS of bent-function sequences are derived. The upper bound improves upon Key's upper bound and the lower bound, obtained through construction, and exceeds
\left(\stackrel{n/2}{n/4}\right)\cdot 2^{n/4}
, where
n
is the length of the shift register generating the
m
-sequence. An interesting general result contained in the derivation is the exhibition of a class of nonlinear sequences whose ELS is guaranteed to be large.