On the Second Descent Points for the K-Error Linear Complexity of 2-Periodic Binary Sequences

In this paper, a constructive approach for determining CELCS (critical error linear complexity spectrum) for the kerror linear complexity distribution of 2-periodic binary sequences is developed via the sieve method and Games-Chan algorithm. Accordingly, the second descent point (critical point) distribution of the k-error linear complexity for 2-periodic binary sequences is characterized. As a by product, it is proved that the maximum k-error linear complexity is 2n-(2l-1) over all 2-periodic binary sequences, where 2l-1<=k < 2l and l < n. With these results, some work by Niu et al. are proved to be incorrect. Keywords-periodic sequence; linear complexity; k-error linear complexity; k-error linear complexity distribution