Dobbertin has embedded the problem of construction of bent functions in a recursive framework by using a generalization of bent functions called Z-bent functions. Following his ideas, we generalize the construction of partial spreads bent functions to partial spreads Z-bent functions of arbitrary level. Furthermore, we show how these partial spreads Z-bent functions give rise to a new construct...

In this paper, we investigate the properties of generalized bent functions defined on Z2 with values in Zq , where q ≥ 2 is any positive integer. We characterize the class of generalized bent functions symmetric with respect to two variables, provide analogues of Maiorana–McFarland type bent functions and Dillon’s functions in the generalized set up. A class of bent functions called generalized...

In this paper we study those bent functions which are linear on elements of spreads, their connections with ovals and line ovals, and we give descriptions of their dual bent functions. In particular, we give a geometric characterization of Niho bent functions and of their duals, we give explicit formula for the dual bent function and present direct connections with ovals and line ovals. We also...

In this paper, the relation between binomial Niho bent functions discovered by Dobbertin et al. and o-polynomials that give rise to the Subiaco and Adelaide classes of hyperovals is found. This allows to expand the class of bent functions that corresponds to Subiaco hyperovals, in the case when m ≡ 2 (mod 4).

In this paper we find a lower bound of the second-order nonlinearities of Boolean bent functions of the form f(x) = Tr 1 (α1x d1 + α2x 2), where d1 and d2 are Niho exponents. A lower bound of the second-order nonlinearities of these Boolean functions can also be obtained by using a result proved by Li, Hu and Gao (eprint.iacr.org/2010 /009.pdf). It is demonstrated that for large values of n the...

Boolean functions which are simultaneously bent and negabent are studied. Transformations that leave the bent-negabent property invariant are presented. A construction for infinitely many bentnegabent Boolean functions in 2mn variables (m > 1) and of algebraic degree at most n is described, this being a subclass of the Maiorana– McFarland class of bent functions. Finally it is shown that a bent...

A one to one correspondence between regular generalized bent functions from Fn2 to Z2m , and m−tuples of Boolean bent functions is established. This correspondence maps selfdual (resp. anti-self-dual) generalized bent functions to m−tuples of self-dual (resp. anti self-dual) Boolean bent functions. An application to the classification of regular generalized bent functions under the extended aff...

BACKGROUND As an important perennial herbaceous flower, Salvia splendens possesses high ornamental value. Understanding its branching processes may help scientists select the best plant type. Although Salvia splendens is a frequently-used horticultural flower, only limited transcriptomic or genomic research is available in public databases. In the present study, we, for the first time, construc...

In this paper we characterize (octal) bent generalized Boolean functions defined on Z2 with values in Z8. Moreover, we propose several constructions of such generalized bent functions for both n even and n odd.