In this paper, for the the primes p such that 3 is a divisor of p − 1, we prove a result which reduces the computation of the linear complexity of a sequence over GF (p m )(any positive integer m) with the period 3n (n and p m −1 are coprime) to the computation of the linear complexities of three sequences with the period n. Combined with some known algorithms such as generalized Games-Chan algorithm, Berlekamp-Massey algorithm and Xiao-Wei-Lam-Imamura algorithm, we can determine the linear

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... lexity of any sequence over GF (p m ) with the period 3n (n and p m − 1 are coprime) more efficiently. Keywords: number theory of the finite field, cryptography, stream cipher, fast algorithm.