Abstract: The linear complexity and the k-error linear complexity of a sequence are used as important measures of keystream strength. By studying linear complexity of binary sequences with period 2n, it is proposed that the computation of k-error linear complexity can be converted to finding error sequences with minimal Hamming weight. In order to study sequence randomness, the k-error sequences distribution that corresponds with the k-error linear complexity of sequence is discussed. Based on Games-Chan algorithm, for k=3, the counting functions on the k-error sequences of 2n-periodic binary sequences with linear complexity2n- are derived and the effectiveness is proved with computer programming.