Summary: The linear complexity and its stability of periodic sequences are of fundamental importance as measure indexes on the security of stream ciphers and the k-error linear complexity reveals the stability of the linear complexity properly. The k-error linear complexity of periodic sequences is defined to be the smallest linear complexity that can be obtained by changing k or fewer bits of the sequence per period. For 2pn-periodic binary sequences, where p is an odd prime and 2 is a primitive root modulo p2, we present and prove the unique expression of the linear complexity. Moreover we show a relationship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity.