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Much work has been devoted to bent functions in odd characteristic, but there still remains a gap between our knowledge of binary and nonbinary bent functions. In the first part of this paper, we attempt to partially bridge this gap by…

Discrete Mathematics · Computer Science 2026-04-20 Claude Carlet , and Alexander Kholosha

Bent-negabent functions have many important properties for their application in cryptography since they have the flat absolute spectrum under the both Walsh-Hadamard transform and nega-Hadamard transform. In this paper, we present four new…

Information Theory · Computer Science 2022-09-20 Fei Guo , Zilong Wang , Guang Gong

Let $\mathbb{F}_{p^{n}}$ be the finite field with $p^n$ elements and $\operatorname{Tr}(\cdot)$ be the trace function from $\mathbb{F}_{p^{n}}$ to $\mathbb{F}_{p}$, where $p$ is a prime and $n$ is an integer. Inspired by the works of…

Information Theory · Computer Science 2021-08-03 Xi Xie , Nian Li , Xiangyong Zeng , Xiaohu Tang , Yao Yao

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…

Combinatorics · Mathematics 2022-07-13 José Andrés Armario , Ronan Egan , Dane Flannery

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

Information Theory · Computer Science 2014-05-23 Jacques Wolfmann

In this paper, we first present a new secondary construction of bent functions (building new bent functions from two already defined ones). Furthermore, we apply the construction using as initial functions some specific bent functions and…

Cryptography and Security · Computer Science 2012-11-20 Fengrong Zhang , Claude Carlet , Yupu Hu , Wenzheng Zhang

Since Kilmer et al. introduced the new multiplication method between two third-order tensors around 2008 and third-order tensors with such multiplication structure are also called as T-product tensors, T-product tensors have been applied to…

Probability · Mathematics 2021-10-06 Shih Yu Chang , Yimin Wei

The dual stable Grothendieck polynomials are a deformation of the Schur functions, originating in the study of the K-theory of the Grassmannian. We generalize these polynomials by introducing a countable family of additional parameters, and…

Combinatorics · Mathematics 2020-09-29 Pavel Galashin , Darij Grinberg , Gaku Liu

The coordinate invariant theory of generalised functions of Colombeau and Meril is reviewed and extended to enable the construction of multi-index generalised tensor functions whose transformation laws coincide with their counterparts in…

General Relativity and Quantum Cosmology · Physics 2007-05-23 J. A. Vickers , J. P. Wilson

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…

Cryptography and Security · Computer Science 2007-05-23 Jianqin Zhou

Generalized bent (gbent) functions is a class of functions $f: \mathbb{Z}_2^n \rightarrow \mathbb{Z}_q$, where $q \geq 2$ is a positive integer, that generalizes a concept of classical bent functions through their co-domain extension. A lot…

Information Theory · Computer Science 2016-11-22 S. Hodžić , E. Pasalic

In the first part of this paper [16], some results on how to compute the flat spectra of Boolean constructions w.r.t. the transforms {I,H}^n, {H,N}^n and {I,H,N}^n were presented, and the relevance of Local Complementation to the quadratic…

Information Theory · Computer Science 2007-07-13 Constanza Riera , George Petrides , Matthew G. Parker

Negabent functions as a class of generalized bent functions have attracted a lot of attention recently due to their applications in cryptography and coding theory. In this paper, we consider the constructions of negabent functions over…

Information Theory · Computer Science 2016-06-30 Gaofei Wu , Nian Li , Yuqing Zhang , Xuefeng Liu

We introduce a way to color the regions of a classical knot diagram using ternary operations, so that the number of colorings is a knot invariant. By choosing appropriate substitutions in the algebras that we assign to diagrams, one obtains…

Geometric Topology · Mathematics 2019-10-29 Maciej Niebrzydowski

Bent functions can be classified into regular bent functions, weakly regular but not regular bent functions, and non-weakly regular bent functions. Regular and weakly regular bent functions always appear in pairs since their duals are also…

Information Theory · Computer Science 2015-11-10 Ayca Cesmelioglu , Wilfried Meidl , Alexander Pott

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.

Combinatorics · Mathematics 2011-03-07 Pante Stanica , Thor Martinsen

The aim of this paper is to study generating functions for the coefficients of the classical superoscillatory function associated with weak measurements. We also establish some new relations between the superoscillatory coefficients and…

Classical Analysis and ODEs · Mathematics 2023-04-03 Fabrizio Colombo , Rolf Soeren Krausshar , Irene Sabadini , Yilmaz Simsek

In this paper, we further investigate properties of generalized bent Boolean functions from $\Z_{p}^n$ to $\Z_{p^k}$, where $p$ is an odd prime and $k$ is a positive integer. For various kinds of representations, sufficient and necessary…

Number Theory · Mathematics 2016-06-09 Libo Wang , Baofeng Wu , Zhuojun Liu

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…

Information Theory · Computer Science 2016-11-22 Lin Sok , MinJia Shi , Patrick Solé

We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. Applying our methods to several field theories such as abelian BF, Chern-Simons and 2-dimensional…

Mathematical Physics · Physics 2008-11-26 Rafael Diaz , Lorenzo Leal