Linear complexity of quaternary sequences constructed from binary Legendre sequences

In this paper, we derive the linear complexity of the quaternary sequences proposed by Kim, Jang, Kim, and No. Because the period of the quaternary sequences is 2p, we introduce the discrete Fourier transform over the finite field F
_qm
which is a splitting field of x
^2p
- 1. It turns out that the linear complexity over F
_qm
of the quaternary sequence constructed from the Legendre sequence is p or 2p - 1.