Reducing the calculation of the linear complexity of u2 v -periodic binary sequences to Games–Chan algorithm

We show that the linear complexity of a u2 ^v -periodic binary sequence, u odd, can easily be calculated from the linear complexities of certain 2 ^v -periodic binary sequences. Since the linear complexity of a 2 ^v -periodic binary sequence can efficiently be calculated with the Games-Chan algorithm, this leads to attractive procedures for the determination of the linear complexity of a u2 ^v -periodic binary sequence. Realizations are presented for u = 3, 5, 7, 15.