On the First and Second Critical Error Linear Complexity of Binary 2ⁿ-periodic Sequences

This paper studies the error linear complexity of binary sequences with period 2ⁿ. One new representation of binary sequences with period 2ⁿ and new interpretation of Games-Chan algorithm are given. New properties about the first critical error linear complexity and one algorithm to compute the first critical error linear complexity are given. One formula of the minimum value k for which the k-error linear complexity is strictly less than the first critical error linear complexity is provided.