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 bisinGF(p^m), bⁿ=-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^tn (such that 2 ^t|p^m-1 and gcd(n,p^m-1)=1) more efficiently