Linear complexity and the k-error linear complexity of periodic sequences are the important security indices of stream cipher systems. This paper focuses on the distribution of p-error linear complexity of p-ary sequences with period pn. For p-ary sequences of period pn with linear complexity pn-p+1, n≥1, we present all possible values of the p-error linear complexity, and derive the exact formulas to count the number of the sequences with any given p-error linear complexity.

The k-error linear complexity of a sequence is a fundamental concept for assessing the stability of the linear complexity. After computing the k-error linear complexity of a sequence, those bits that cause the linear complexity reduced also need to be determined. For binary sequences with period 2pn, where p is an odd prime and 2 is a primitive root modulo p2, we present an algorithm which computes the minimum number k such that the k-error linear complexity is not greater than a given constant c. The corresponding error sequence is also obtained.

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. Recently, Zhou designed an algorithm for computing the k-error linear complexity of 2pn periodic sequences over GF(q). In this paper, we develop a genetic algorithm to confirm that one can't get the real k-error linear complexity for some sequenes by the Zhou's algorithm. Analysis indicates that the Zhou's algorithm is unreasonable in some steps. The corrected algorithm is presented. Such algorithm will increase the amount of computation, but is necessary to get the real k-error linear complexity. Here p and q are odd prime, and q is a primitive root (mod p2).

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.

We discuss a typical profile of the k-error linear complexity for balanced binary exponent periodic sequences and the number of periodic distinct sequences by their profiles. A numerical example with period 16 is also shown.