An algorithm for the k-error linear complexity of a sequence with period 2pn over GF(q)

We first optimize the structure of the Wei-Xiao-Chen algorithm for the linear complexity of sequences over GF(q) with period N = 2pⁿ, where p and q are odd primes, and q is a primitive root ( mod p²). Then the union cost is used, so that an efficient algorithm for computing k-error linear complexity of a sequence with period 2pⁿ over GF(q) is derived, where p and q are odd primes, and q is a primitive root of modulo p². We also give a validity proof of the proposed algorithm. Finally, a numerical example is presented to illustrate the algorithm.