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.

A (1,-1)-matrix will be called a bent type matrix if each row and each column are bent sequences. A similar description can be found in Carlisle M. in which the authors use the properties of bent type matrices to construct a class of bent functions. In this paper we give a general method to construct bent type matrices and show that the bent sequence obtained from a bent type matrix is a genera...

BACKGROUND Hepatic fibrosis is characterised by a progressive accumulation of fibrillar extracellular matrix (ECM) proteins, including collagen that occurs in chronic liver diseases. Transforming growth factor-beta1 (TGF-beta)/Smad3 signalling plays a major role in tissue fibrogenesis acting as a potent stimulus of ECM accumulation. AIM To evaluate the effects of a combined therapy with anti-...

Salvia miltiorrhiza, which is commonly known as Danshen, is a traditional Chinese herbal medicine. To illustrate its physiological and biochemical responses to salt stress and to evaluate the feasibility of cultivating this plant in saline coastal soils, a factorial experiment under hydroponic conditions was arranged on the basis of a completely randomised design with three replications. Five s...

Salvia miltiorrhiza is an important medicinal plant with great economic and medicinal value. The complete chloroplast (cp) genome sequence of Salvia miltiorrhiza, the first sequenced member of the Lamiaceae family, is reported here. The genome is 151,328 bp in length and exhibits a typical quadripartite structure of the large (LSC, 82,695 bp) and small (SSC, 17,555 bp) single-copy regions, sepa...

Bent functions as optimal combinatorial objects are difficult to characterize and construct. In the literature, bent idempotents are a special class of bent functions and few constructions have been presented, which are restricted by the degree of finite fields and have algebraic degree no more than 4. In this paper, several new infinite families of bent functions are obtained by adding the the...

In this paper, we consider the characterization of the bentness of quadratic Boolean functions of the form f(x) = ∑ m 2 −1 i=1 Tr n 1 (cix 1+2ei)+Tr n/2 1 (cm/2x 1+2n/2), where n = me, m is even and ci ∈ GF (2 ). For a general m, it is difficult to determine the bentness of these functions. We present the bentness of quadratic Boolean function for two cases: m = 2p and m = 2pq, where p and q ar...

We obtain the nonexistence of generalized bent functions (GBFs) from (\ZZ/t\ZZ)^n to \ZZ/t\ZZ (called type [n,t]), for a large new class. Specifically, by showing certain quadratic norm form equations have no integral points, we obtain the universal nonexistence of GBFs with type [n, 2p^e] for all sufficiently large p with respect to n and (p-1)/\ord_2(p), and by computational methods with a we...