Recent developments in word-based stream ciphers present the study on multisequences. The joint linear complexity and k-error joint linear complexity are fundamental concepts for the assessment of multisequences. The k-error joint linear complexity spectrum contains all the information about how the joint linear complexity of a multisequence decreases as the number k of allowed bit changes increases. In this paper, we present an efficient algorithm by which the k-error joint linear complexity spectrum for a t-fold pn-periodic binary multisequence can be entirely determined using O(tpnlogp)$\mathcal {O}(tp^{n}\log p)$ bit operations, where p is an odd prime, 2 is a primitive root modulo p2 and n is a positive integer.