On the k-error linear complexity of sequences with period 2pn over G F (q)

In this paper, we first optimize the structure of the Wei-Xiao-Chen algorithm for the linear complexity of sequences over GF(q) with period N = 2p (n) , where p and q are odd primes, and q is a primitive root modulo p (2). The second, an union cost is proposed, so that an efficient algorithm for computing the k-error linear complexity of a sequence with period 2p (n) over GF(q) is derived, where p and q are odd primes, and q is a primitive root modulo p (2). The third, we give a validity of the proposed algorithm, and also prove that there exists an error sequence e (N) , where the Hamming weight of e (N) is not greater than k, such that the linear complexity of (s + e) (N) reaches the k-error linear complexity c. We also present a numerical example to illustrate the algorithm. Finally, we present the minimum value k for which the k-error linear complexity is strictly less than the linear complexity.