In this paper, using bent functions defined on the finite field, we generalized the construction method of the family of p-ary bent sequences with balanced and optimal correlation property introduced by Kumar and Moreno for an odd prime p [3], called a generalized p-ary bent sequence. It turns out that the family of balanced p-ary sequences with optimal correlation property introduced by Moriuc...

For weakly regular bent functions in odd characteristic the dual function is also bent. We analyse a recently introduced construction of nonweakly regular bent functions and show conditions under which their dual is bent as well. This leads to the definition of the class of dual-bent functions containing the class of weakly regular bent functions as a proper subclass. We analyse self-duality fo...

The characterization and construction of bent functions are challenging problems. The paper generalizes the constructions of Boolean bent functions by Mesnager [33], Xu et al. [40] and p-ary bent functions by Xu et al. [41] to the construction of p-ary weakly regular bent functions and presents new infinite families of p-ary weakly regular bent functions from some known weakly regular bent func...

We give a construction of 3-class and 4-class association schemes from s-nonlinear and differentially 2s-uniform functions, and a construction of p-class association schemes from weakly regular p-ary bent functions, where p is an odd prime.

In this paper, we investigate the constructions of generalized bent Boolean functions defined on with values in Z4. We first present a construction of generalized bent Boolean functions defined on with values in Z4. The main technique is to utilize bent functions to derive generalized bent functions on odd number of variables. In addition, by using Boolean permutations, we provide a specific me...

In this paper, we present a new class of semi-bent quadratic Boolean functions of the form f(x) = ∑⌊m−1 2 ⌋ i=1 Tr n 1 (cix 1+4i) (ci ∈ F4,n = 2m). We first characterize the semi-bentness of these quadratic Boolean functions. There exists semi-bent functions only when m is odd. For the case: m = p, where p is an odd prime with some conditions, we enumerate the semi-bent functions. Further, we g...

In this paper, we propose two classes of 2k-variable Boolean functions, which have optimal algebraic immunity under the assumption that a general combinatorial conjecture is correct. These functions also have high algebraic degree and high nonlinearity. One class contain more bent functions, and the other class are balanced.