An efficient algorithm for determining the linear complexity and the minimal polynomial of a sequence with period 2pmqn over a finite field GF(q) is proposed, where p and q are primes, and q is a primitive root modulo p2. The new algorithm generalizes the algorithm for computing the linear complexity of a sequence with period qn over GF(q) and the algorithm for computing one of a sequence with period 2pm over GF(q).
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