We construct two families of binary quadratic bent functions in a combinatorial way. They are self-dual and anti-self-dual quadratic bent functions, respectively, which are not of the Maiorana-McFarland type, but affine equivalent to it.

Starting from special near-bent functions in dimension 2t − 1 we construct bent functions in dimension 2t having a specific derivative. We deduce new families of bent functions.

We obtain new nonexistence results of generalized bent functions from Z q to Zq (called type [n, q]) in the case that there exist cyclotomic integers in Z[ζq ] with absolute value q n 2 . This result generalize the previous two scattered nonexistence results [n, q] = [1, 2×7] of Pei [13] and [3, 2 × 23] of Jiang-Deng [7] to a generalized class. In the last section, we remark that this method ca...

We get two kinds of new results on nonexistence of generalized bent function. The first one is Based on Feng’s results by using Schmidt’s field descent method. For the second kind, considering special property of the fieldQ(ζ23e), We get new nonexistence results of generalized bent functions with type [3, 2 · 23].

It is well known that the degree of a 2m-variable bent function is at most m. However, the case in homogeneous bent functions is not clear. In this paper, it is proved that there is no homogeneous bent functions of degree m in 2m variables when m > 3; there is no homogenous bent function of degree m− 1 in 2m variables when m > 4; Generally, for any nonnegative integer k, there exists a positive...

Two (so-called C,D) classes of permutation-based bent Boolean functions were introduced by Carlet two decades ago, but without specifying some explicit construction methods for their construction (apart from the subclass D0). In this article, we look in more detail at the C class, and derive some existence and nonexistence results concerning the bent functions in the C class for many of the kno...

In this paper, we classify all formally self-dual Boolean functions and self-dual bent functions under the action of the extended symmetric group in 2, 4 variables, and give a lower bound for the number of non-equivalent functions in 6 variables. There are exactly 2, 91 (1, 3 respectively) and at least 5535376 representatives from equivalence class of formally self-dual Boolean functions (self-...

Several nonexistence results on generalized bent functions f : Zn 2 → Zm presented by using some knowledge on cyclotomic number fields and their imaginary quadratic subfields.

It is well-known that degree two finite field extensions can be equipped with a Hermitian-like structure similar to the extension of the complex field over the reals. In this contribution, using this structure, we develop a modular character theory and the appropriate Fourier transform for some particular kind of finite Abelian groups. Moreover we introduce the notion of bent functions for fini...

Synergistic activity of Salvia officinalis and Cichorium intybus extracts and commonly used antibiotics, amoxicillin and chloramphenicol, were evaluated. Interactions between plant extracts and antibiotics were tested by checkerboard method and interpreted as FIC index. Staphylococcus aureus ATCC 25923, Escherichia coli ATCC 25922, Pseudomonas aeruginosa ATCC 27853 and clinical isolates Staphyl...