The k-error linear complexity and the linear complexity of the keystream of a stream cipher are two important standards to scale the randomness of the key stream. For a pq~n-periodic binary sequences where p, q are two odd primes satisfying that 2 is a primitive root module p and q~2 and gcd(p-1 , q-1)=2, we analyze the relationship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity. The k-error linear complexity and the linear complexity of the keystream of a stream cipher are two important standards to scale the randomness of the key stream. For a pq ~ n-periodic binary sequences where p, q are two odd primes satisfying that 2 is a primitive root module p and q ~ 2 and gcd (p-1, q-1) = 2, we analyze the relationship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity.