New constructions of low-correlation sequences with high-linear complexity

In this study, the authors propose a new concept named similar-bent function and the authors present two general methods to construct balanced sequences with low correlation by using similar-bent functions and orthogonal similar-bent functions. The authors find that the bent sequence sets are special cases of our construction. The authors also investigate the linear complexity of the new constructed sequences. If a suitable similar-bent function is given, the sequences constructed by it can have high-linear complexity. As examples, the authors construct two new low-correlation sequence sets. One constructed based on Dobbertin´s iterative function is asymptotically optimal with respect to the Welch bound and the other one is constructed based on Kasami function whose sequences have a high-linear complexity.