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 Fqm which is a splitting field of x2p − 1. It turns out that the linear complexity over Fqm of the quaternary sequence constructed from the Legendre sequence is p or 2p − 1.
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