Related papers: Bent Rectangles
We propose a representation of boolean bent functions by bent rectangles, that is, by special matrices with restrictions on rows and columns. Using this representation, we exhibit new classes of bent functions, give an algorithm to…
A one to one correspondence between regular generalized bent functions from $\F_2^n$ to $\Z_{2^m},$ and $m-$tuples of Boolean bent functions is established. This correspondence maps self-dual (resp. anti-self-dual) generalized bent…
In a recent survey, Schmidt compiled equivalences between generalized bent functions, group invariant Butson Hadamard matrices, and abelian splitting relative difference sets. We establish a broader network of equivalences by considering…
Based on the definition of generalized partially bent functions, using the theory of linear transformation, the relationship among generalized partially bent functions over ring Z N, generalized bent functions over ring Z N and affine…
In 1999 Bernasconi and Codenotti noted that the Cayley graph of a bent function is strongly regular. This paper describes the concept of extended Cayley equivalence of bent functions, discusses some connections between bent functions,…
Generalisations of the bent property of a boolean function are presented, by proposing spectral analysis with respect to a well-chosen set of local unitary transforms. Quadratic boolean functions are related to simple graphs and it is shown…
In this article a procedure to construct bent functions from $\F_{p^n}$ to $\F_p$ by merging plateaued functions which are bent on ($n-2$)-dimensional subspaces of $\F_{p^n}$ is presented. Taking advantage of such classes of plateaued…
We provide constructions of bent functions using triples of permutations. This approach is due to Mesnager. In general, involutions have been mostly considered in such a machinery; we provide some other suitable triples of permutations,…
In this paper we characterize (octal) bent generalized Boolean functions defined on $\BBZ_2^n$ with values in $\BBZ_8$. Moreover, we propose several constructions of such generalized bent functions for both $n$ even and $n$ odd.
We present a unified framework for representing commutative rings through affine algebraic theories and Boolean rings through hyperaffine algebraic theories. This yields categorical equivalences between these theories and, respectively,…
We will introduce formal frames of manifolds, which are a generalization of ordinary frames. Their fundamental properties are discussed. In particular, canonical forms are introduced, and torsions are defined in terms of them as a…
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation…
We present the notion of a filtered bundle as a generalisation of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more…
In this work, we employ the concept of {\em composite representation} of Boolean functions, which represents an arbitrary Boolean function as a composition of one Boolean function and one vectorial function, for the purpose of specifying…
This is a review with examples concerning the concepts of affine (in particular, constant and linear) vector fields and fundamental vector fields on a manifold. The affine, linear and constant vector fields on a manifold are shown to be in…
Bent functions are Boolean functions that are maximally nonlinear. They can be represented as bent squares, i.e., square matrices for which each row and each column is the Walsh spectrum of a Boolean function. Using this representation, it…
In this letter, we give a characterization for a generic construction of bent functions. This characterization enables us to obtain another efficient construction of bent functions and to give a positive answer on a problem of bent…
We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…
Bent functions are balanced by restricting their domains to vectors with either even or odd Hamming weights, which ensures an equal number of pre-images for both, 0 and 1. Using the previous fact, we can construct bent functions on two…
A class of spherical functions is studied which can be viewed as the matrix generalization of Bessel functions. We derive a recursive structure for these functions. We show that they are only special cases of more general radial functions…