I. Introduction
The linear complexity of a binary periodic sequence , denoted by , is defined as the length of the shortest linear feedback shift register that generates , or alternatively the smallest nonnegative integer for which there exist coefficients in the finite field such that s_{i} + d_{1}s_{i-1} +\cdots + d_{L}s_{i-L} = 0 ,\qquad {\hbox{for all}}~ i \ge L.