Adams, C. We introduce two general classes of bent sequences, " bent-based " and " linear-based " , and conjecture that all bent sequences fall into these classes. This gives us a framework for discussing the construction and cardinality of the set of bent sequences of any given order.

In a recent paper [1], it is shown that the restrictions of bent functions to subspaces of codimension 1 and 2 are highly nonlinear. Here, we present an extensive study of the restrictions of bent functions to affine subspaces. We propose several methods which are mainly based on properties of the derivatives and of the dual of a given bent function. We solve an open problem due to Hou [2]. We ...

In this paper we introduce a sequence of discrete Fourier transforms and define new versions of bent functions, which we shall call (weak, strong) octa/hexa/2-bent functions. We investigate relationships between these classes and completely characterize the octabent and hexabent functions in terms of bent functions.

Search of rich boolean function for designing a good cryptosystem is most important. In this search from the infinite domain of integers, cases where rejection of integers for the existence of Generalized bent function is very helpfull. With the help of some necessary condition of GBF here we show the non existence of [n,5] type Generalized Bent functions.

We present new abelian partial difference sets and amorphic group schemes of both Latin square type and negative Latin square type in certain abelian p-groups. Our method is to construct what we call pseudo-quadratic bent functions and use them in place of quadratic forms. We also discuss a connection between strongly regular bent functions and amorphic group schemes.

In this note we prove that bent functions can be precisely characterized in terms of a special class of strongly regular graphs, thus providing a positive answer to a question raised in the paper Spectral Analysis of Boolean Functions as a Graph Eigenvalue Problem. (After publication of the above paper by the rst two authors, the third sent them a remark showing that bent functions are exactly ...

For each non-constant q in the set of n-variable Boolean functions, the qtransform of a Boolean function f is related to the Hamming distances from f to the functions obtainable from q by nonsingular linear change of basis. Klapper conjectured that no Boolean function exists with its q-transform coefficients equal to ±2n/2 (such function is called q-bent). In our early work, we only gave partia...

In [2] some results on PS bent functions were recently published. With the help of an alternative proof for the degree of a subclass of PS bent functions, we show that most of the results presented in [2] cannot be applied to the whole class of PS bent functions, but only to a subset of such bent functions.

In this paper, the response surface methodology (RSM) and finite element (FE) simulation were applied to optimize push-bending process parameters of thin-walled tube with polyurethane mandrel. The objective present work is predict optimal set including length diameter ratio mandrel (L/D), friction coefficient between die ( $${\mu }_{1}$$ ), }_{2}$$ Poisson’s $$\upsilon$$ ) obtain qualified bent...

We prove that, for bent vectorial functions, CCZ-equivalence coincides with EA-equivalence. However, we show that CCZ-equivalence can be used for constructing bent functions which are new up to CCZequivalence. Using this approach we construct classes of nonquadratic bent Boolean and bent vectorial functions.