We prove that cubic homogeneous bent functions f : V2n → GF(2) exist for all n ≥ 3 except for n = 4.

We introduce the notion of a bent function on a finite nonabelian group which is a natural generalization of the well-known notion of bentness on a finite abelian group due to Logachev, Salnikov and Yashchenko. Using the theory of linear representations and noncommutative harmonic analysis of finite groups we obtain several properties of such functions similar to the corresponding properties of...

In this paper, a new construction of quaternary bent functions from quaternary quadratic forms over Galois rings of characteristic 4 is proposed. Based on this construction, several new classes of quaternary bent functions are obtained, and as a consequence, several new classes of quadratic binary bent and semi-bent functions in polynomial forms are derived. This work generalizes the recent wor...

Two new results on the nonexistence of generalized bent functions are presented by using properties of the decomposition law of primes in cyclotomic fields and properties of solutions of some Diophantine equations, and examples satisfying our results are given.

The minimum distance between Bent functions and Resilient functions is studied. An algorithm for calculating the minimum distance betw een Bent functions and resilient functions is given. We give a new lower bound for the minimum distance be tween Bent functions and 1 resilient functions. This new lower bound is better than that presented by S. Maity etc in 2004, and their conjectures are prove...

We present a new characterization of semi-bent and bent quadratic functions on finite fields. First, we determine when a GF (2)-linear combination of Gold functions Tr(x i+1) is semi-bent over GF (2), n odd, by a polynomial GCD computation. By analyzing this GCD condition, we provide simpler characterizations of semi-bent functions. For example, we deduce that all linear combinations of Gold fu...

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 an analogue of Maiorana– McFarland type bent functions in the generalized set up. A class of bent functions called generalized spreads type is introd...

In this presentation a technique for constructing bent functions from plateaued functions is introduced. This generalizes earlier techniques for constructing bent from near-bent functions. Analysing the Fourier spectrum of quadratic functions we then can construct weakly regular as well as non-weakly regular bent functions both in even and odd dimension. This type of functions yield the first k...

methanolic extracts of five native species of salvia from the labiatae family were evaluated for antioxidant activity in low-erucic acid rapeseed oil using the schaal oven test at 60°c, with deterioration monitored by determination of peroxide value, conjugated diene content and p-anisidine value. the activity of the salvia extracts was compared with that of tbhq, ascorbyl palmitate, and extrac...