Let
r be an odd prime, such that
r≥5 and
r≠
p,
m be the order of
r modulo
p. Then, there exists a 2
pth root of unity in the extension field F
rm. Let
G(
x) be the generating polynomial of the considered quaternary sequences over F
q[x] with
q=
rm. By explicitly computing the number of zeros of the generating polynomial
G(
x) over F
rm, we can determine the degree of the minimal polynomial, of the quaternary sequences which in turn represents the linear complexity. In this paper, we show that the minimal value of the linear complexity is equal to $ \frac{1}{2}(3p-1) $ which is more than
p, the half of the period 2
p. According to Berlekamp-Massey algorithm, these sequences viewed as enough good for the use in cryptography.
抄録全体を表示