Proof of Rueppel's linear complexity conjecture (Corresp.)

Rueppel has conjectured that, for all
n\geq 1
, the subsequence consisting of the first
n
digits of the binary sequence
(1,1,0,1,0,0,0,1,0^{7},1,0^{15},1, \cdots )
has linear complexity
\lfloor (n + 1)/2 \rightfloor
. This conjecture is proved, and a minimum length generator is found for each
n
. The proof utilizes properties of an element in an extension field of the field of rational functions over GF
(2)
.