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Abstract. In this paper, we propose a new concept named similar-bent function and we present two general methods to construct balanced sequences with low correlation by using similar-bent functions and orthogonal similar-bent functions. We find that the bent sequence sets are special cases of our construction. We 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, we construct two new low correlation sequence sets. One constructed based on Dobbertin's iterative function is asymptotically optimal with respect to Welch's bound and the other one is constructed based on Kasami function whose sequences have a high linear complexity.

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In this paper, we give some results towards the conjecture that σ 2 t+1 l−1,2 t are the only nonlinear balanced elementary symmetric Boolean functions where t and l are positive integers. At first, a unified and simple proof of some earlier results is shown. Then a property of balanced elementary symmetric Boolean functions is presented. With this property, we prove that the conjecture is true for n = 2 m + 2 t − 1 where m, t(m > t) are two non-negative integers, which verified the conjecture for a large infinite class of integer n.