Fast Algorithms for Determining the Linear Complexity of Period Sequences

We introduce a fast algorithm for determining the linear complexity and the minimal polynomial of a sequence with period pn over GF(q), where p is an odd prime, q is a prime and a primitive root modulo p2; and its two generalized algorithms. One is the algorithm for determining the linear complexity and the minimal polynomial of a sequence with period pmqn over GF(q), the other is the algorithm for determining the k-error linear complexity of a sequence with period pn over GF(q), where p is an odd prime, q is a prime and a primitive root modulo p2. The algorithm for determining the linear complexity and the minimal polynomial of a sequence with period 2pn over GF(q) is also introduced. where p and q are odd prime, and q is a primitive root (mod p2). These algorithms uses the fact that in these case the factorization of xN - 1 is especially simple for N = pn, 2pn, pn qm.

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