Analysis of the Minerror of the pn-Periodic Sequences

To ensure the security of the data during transmission, the data should be encrypted by a key stream sequence which should be strong enough with good randomness and unpredictability. Cryptographically strong sequences should not only have a large linear complexity, but also the change of a few terms should not cause a significant decrease of the linear complexity. This requirement leads to the theory of the stability of linear complexity. K-error linear complexity reflects the stability of the linear complexity properly. In this paper, by analyzing the relationship between the linear complexity and the k-error linear complexity of pⁿ- periodic sequence, we studied the upper bound of minerror, i.e. the minimum value k for which the k-error linear complexity is strictly less than the linear complexity. Here p is an odd prime, and q is a prime and a primitive root (mod p²).