Linear complexity of quaternary sequences constructed from binary Legendre sequences
Young Sik Kim, Ji-Woong Jang, Sang‐Hyo Kim, Jong‐Seon No · International Symposium on Information Theory and its Applications · 2012
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 x2p − 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.