Fast algorithms for determining the linear complexity of sequences over GF (pm) with period 2tn

We prove a result which reduces the computation of the linear complexity of a sequence over GF (p(m)) (p is an odd prime) with period 2n (n is a positive integer such that there exists an element b is an element of GF (p(m)), b(n) = -1) to the computation of the linear complexities of two sequences with period n. By combining with some known algorithms such as the Berlekamp-Massey algorithm and the Games-Chan algorithm we can determine the linear complexity of any sequence over GF (p(m)) with period 2(t)n (such that 2(t)vertical bar p(m) - 1 and gcd(n, p(m) - 1) = 1) more efficiently.