On the Linear Complexity of Binary Sequences of Period $4N$ With Optimal Autocorrelation Value/Magnitude
Nian Li, Xiaohu Tang · IEEE Transactions on Information Theory · 2011
Three classes of binary sequences of period 4Nwith optimal autocorrelation value/magnitude have been constructed by Tang and Gong based on interleaving certain kinds of sequences of periodN, i.e., the Legendre sequence, twin-prime sequence and generalized GMW sequence. In this paper, by means of sequence polynomials of the underlying sequences, the properties of roots of the corresponding sequence polynomials of the interleaved sequences with period 4Nand optimal autocorrelation value/magnitude are discussed in the splitting field ofxN-1 . As a consequence, both the minimal polynomials and linear complexities of these three classes of sequences are completely determined except for the case of the sequences obtained from the generalized GMW sequences. For the latter, the minimal polynomial and linear complexity can be specially obtained if the sequence is constructed based onm-sequences instead of generalized GMW sequences.