Fast algorithms for determining the linear complexity of sequences over GF(p/sup m/) with period 2/sup t/n

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
), 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
|p
^m
-1 and gcd(n,p
^m
-1)=1) more efficiently